M. A. Aizerman and F. R. Gantmacher, Absolute stability of control systems, 1964.

B. D. Anderson, N. K. Bose, and E. I. Jury, Output feedback stabilization and related problems-solution via decision methods, IEEE Transactions on Automatic Control, vol.20, issue.1, pp.53-66, 1975.
DOI : 10.1109/TAC.1975.1100846

P. Apkarian and H. D. Tuan, Concave programming in control theory, Journal of Global Optimization, vol.15, issue.4, pp.343-370, 1999.
DOI : 10.1023/A:1008385006172

P. Apkarian and H. D. Tuan, A sequential SDP/Gauss-Newton algorithm for rankconstrained LMI problems, Proceedings of the Conference on Decision and Control, pp.2328-2333, 1999.

P. Apkarian and H. D. Tuan, Robust control via concave minimization local and global algorithms, IEEE Transactions on Automatic Control, vol.45, issue.2, pp.299-305, 2000.
DOI : 10.1109/9.839953

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.5454

P. Apkarian and H. D. Tuan, Parameterized LMIs in Control Theory, SIAM Journal on Control and Optimization, vol.38, issue.4, pp.1241-1264, 2000.
DOI : 10.1137/S036301299732612X

D. Arzelier, D. Henrion, and D. Peaucelle, Robust D stabilization of a polytope of matrices, International Journal of Control, vol.49, issue.10, pp.744-752, 2002.
DOI : 10.1080/00207178708933721

D. Arzelier and D. Peaucelle, An iterative method for mixed H/sub 2//H/sub ???/ synthesis via static output-feedback, Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002.
DOI : 10.1109/CDC.2002.1184411

D. Arzelier, Lecture on semidefinite programming, 2002.

D. Arzelier, D. Peaucelle, and S. Salhi, Robust static output feedback stabilization for polytopic uncertain systems: Improving the guaranteed performance bound, Proceedings of the IFAC ROCOND, 2003.

D. Arzelier13, ]. A. Astolfi, and P. Colaneri, Static output feedback stabilization: From linear to nonlinear and back " , in Nonlinear Control in the Year 2000, 2000.

V. Balakrishnan and S. Boyd, Global Optimization in Control System Analysis and Design, Control and Dynamic Systems: Advances in Theory and Aplications, pp.1-56, 1992.
DOI : 10.1016/B978-0-12-012753-5.50006-5

V. Balakrishnan, S. Boyd, and S. Balemi, Branch and bound algorithm for computing the minimum stability degree of parameter-dependent linear systems, International Journal of Robust and Nonlinear Control, vol.36, issue.4, pp.295-317, 1992.
DOI : 10.1002/rnc.4590010404

V. Balakrishnan and L. Vandenberghe, Semidefinite programming duality and linear time-invariant systems, IEEE Transactions on Automatic Control, vol.48, issue.1, pp.30-41, 2003.
DOI : 10.1109/TAC.2002.806652

J. A. Ball and J. W. Helton, A Beurling-Lax theorem for the Lie group (U (m, n) which contains most classical interpolation theory, Journal of Operator Theory, vol.9, pp.107-142, 1983.

D. Banjerdpongchai and J. P. How, Convergence analysis of a parametric robust H/sub 2/ controller synthesis algorithm, Proceedings of the 36th IEEE Conference on Decision and Control, pp.2602-2607, 1997.
DOI : 10.1109/CDC.1997.657580

B. R. Barmish and C. V. Hollot, Counter-example to a recent result on the stability of interval matrices by S. Bialas, International Journal of Control, vol.37, issue.5, pp.1103-1104, 1984.
DOI : 10.1080/00207178408933235

B. R. Barmish, Necessary and sufficient conditions for quadratic stabilizability of an uncertain linear system, Journal od Optimization Theory and Applications, vol.46, issue.4, 1985.

B. R. Barmish and C. L. Demarco, A new method for improvement of robustness bounds for linear state equations, Proceedings of the Conference on Information Sciences and Systems, 1986.

B. R. Barmish, M. Fu, and S. Saleh, Stability of a polytope of matrices: counterexamples, IEEE Transactions on Automatic Control, vol.33, issue.6, pp.569-572, 1988.
DOI : 10.1109/9.1254

B. R. Barmish, New tools for robustness analysis, Proceedings of the 27th IEEE Conference on Decision and Control, 1988.
DOI : 10.1109/CDC.1988.194259

B. R. Barmish, New Tools for Robustness of Linear Systems, 1994.

B. R. Barmish, C. A. Floudas, C. V. Hollot, and R. Tempo, A global linear programming solution to some open robustness problems including matrix polytope stability, Proceedings of 1995 American Control Conference, ACC'95, 1995.
DOI : 10.1109/ACC.1995.533867

A. Barvinok, A course in convexity, Graduate Studies in Mathematics, vol.54, 2002.
DOI : 10.1090/gsm/054

M. S. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms, Series in Discrete Mathematics and Optimization, 1993.
DOI : 10.1002/0471787779

C. Beck, Minimality for uncertain systems and IQCs, Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994.
DOI : 10.1109/CDC.1994.411314

C. Beck and R. , Computational study and comparisons of LFT reducibility methods, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), 1998.
DOI : 10.1109/ACC.1998.703562

R. E. Bellman, Introduction to matrix analysis, 1970.

K. P. Bennett and O. L. Mangasarian, Bilinear separation of two sets inn-space, Computational Optimization and Applications, vol.1, issue.2, pp.207-227, 1993.
DOI : 10.1007/BF01299449

A. Ben-tal and A. Nemirovskii, Lectures on modern convex optimization: Analysis, algorithms and engineering applications, MPS-SIAM Series on Optimization, 2001.
DOI : 10.1137/1.9780898718829

R. E. Benton and D. Smith, A non-iterative LMI-based algorithm for robust static-output-feedback stabilization, International Journal of Control, vol.72, issue.14, pp.1322-1330, 1999.
DOI : 10.1080/002071799220290

E. Beran, L. Vandenberghe, and S. Boyd, A global BMI algorithm based on the generalized Benders decomposition, Proceedings of the European Control Conference, 1997.

D. S. Bernstein and W. M. Haddad, LQG control with an H/sup infinity / performance bound: a Riccati equation approach, IEEE Transactions on Automatic Control, vol.34, issue.3, pp.293-305, 1989.
DOI : 10.1109/9.16419

J. Bernussou, P. L. Peres, and J. C. , A linear programming oriented procedure for quadratic stabilization of uncertain systems, Systems & Control Letters, vol.13, issue.1, pp.65-72, 1989.
DOI : 10.1016/0167-6911(89)90022-4

S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, ROBUST CONTROL: THE PARAMETRIC APPROACH, 1995.
DOI : 10.1016/B978-0-08-042230-5.50016-5

S. Bialas, A necessary and sufficient condition for stability of interval matrices, International Journal of Control, vol.37, issue.5, pp.1103-1104, 1983.

P. A. Bliman, A Convex Approach to Robust Stability for Linear Systems with Uncertain Scalar Parameters, SIAM Journal on Control and Optimization, vol.42, issue.6, pp.2016-2042, 2004.
DOI : 10.1137/S0363012901398691

URL : https://hal.archives-ouvertes.fr/inria-00072271

P. A. Bliman, An existence result for polynomial solutions of parameter-dependent LMIs, Systems & Control Letters, vol.51, issue.3-4, pp.165-169, 2004.
DOI : 10.1016/j.sysconle.2003.08.001

URL : https://hal.archives-ouvertes.fr/inria-00071788

V. Blondel and M. Gevers, Simultaneous stabilizability of three linear systems is rationally undecidable, Mathematics of Control, Signals, and Systems, vol.10, issue.2, pp.135-145, 1994.
DOI : 10.1007/BF01211744

V. Blondel and J. Tsitsiklis, NP-Hardness of Some Linear Control Design Problems, SIAM Journal on Control and Optimization, vol.35, issue.6, pp.2118-2127, 1997.
DOI : 10.1137/S0363012994272630

V. Blondel, E. D. Sontag, M. Vidyasagar, and J. C. Willems, Open problems in mathematical systems and control theory, 1999.
DOI : 10.1007/978-1-4471-0807-8

S. Boyd and L. Vandenberghe, Semidefinite Programming Relaxations of Non-Convex Problems in Control and Combinatorial Optimization, Communications, Computation , Control and Signal Processing: A Tribute, 1997.
DOI : 10.1007/978-1-4615-6281-8_15

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

A. Brønsted, An introduction to convex polytopes, 1982.

J. V. Burke, A. S. Lewis, and M. L. Overton, Two numerical methods for optimizing matrix stability, Linear Algebra and its Applications, vol.351, issue.352, pp.351-352117, 2002.
DOI : 10.1016/S0024-3795(02)00260-4

J. V. Burke, A. S. Lewis, and M. L. Overton, A nonsmooth, nonconvex optimization approach to robust stabilization by static output feedback and low-order controllers, Proceedings of Robust Control Design IFAC Symposium, 2003.

J. V. Burke, A. S. Lewis, and M. L. Overton, A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization, SIAM Journal on Optimization, vol.15, issue.3, 2003.
DOI : 10.1137/030601296

Y. Cao, J. Lam, and Y. Sun, Static output feedback simultaneous stabilization: ILMI approach, International Journal of Control, vol.70, issue.5, pp.1641-1645, 1998.
DOI : 10.1080/002071798222145

E. B. Castelan, J. C. Hennet, and E. R. Villareal, Quadratic characterization and use of output stabilizable subspaces, IEEE Transactions on Automatic Control, vol.48, issue.4, 2003.
DOI : 10.1109/TAC.2003.809774

J. Cea and R. Glowinski, Sur des m??thodes d'optimisation par relaxation, Revue fran??aise d'automatique informatique recherche op??rationnelle. Math??matique, vol.7, issue.R3, pp.5-32, 1973.
DOI : 10.1051/m2an/197307R300051

URL : http://www.numdam.org/article/M2AN_1973__7_3_5_0.pdf

W. H. Chen, On relationship between quadratic and robust stability of uncertain systems, International Journal of Robust and Nonlinear Control, vol.4, issue.1, pp.51-58, 1999.
DOI : 10.1002/(SICI)1099-1239(199901)9:1<51::AID-RNC393>3.0.CO;2-A

J. D. Cobb and C. L. Demarco, The minimal dimension of stable faces required to guarantee stability of a matrix polytope, IEEE Transactions on Automatic Control, vol.34, issue.9, 1989.

J. Collado and R. Lozano, Robust stability of the convex-hull of matrices using the polar decomposition, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000.
DOI : 10.1109/ACC.2000.877039

P. Colaneri, J. C. Geromel, and A. Locatelli, Control Theory and design: An RH 2 and RH ? perspective, 1997.

G. E. Coxson and C. L. Demarco, Testing robust stability of general matrix polytope is an N P-hard computation, Proceedings of the Allerton Conference, 1991.

C. A. Crusius and A. Trofino, Sufficient LMI conditions for output feedback control problems, IEEE Transactions on Automatic Control, vol.44, issue.5, 1999.
DOI : 10.1109/9.763227

S. Dasgupta, G. Chockalingam, B. D. Anderson, and M. Fu, Lyapunov functions for uncertain systems with applications to the stability of time varying systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.41, issue.2, 1994.
DOI : 10.1109/81.269046

M. Dettori and C. Scherer, Robust stability analysis for parameter dependent systems using full block S-procedure, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998.
DOI : 10.1109/CDC.1998.757879

J. Doyle, Guaranteed margins for LQG regulators, IEEE Transactions on Automatic Control, vol.23, issue.4, pp.756-757, 1978.
DOI : 10.1109/TAC.1978.1101812

J. C. Doyle, Synthesis of robust controllers and filters with structured plant uncertainty, Proceedings of the Conference on Decision and Control, pp.109-114, 1983.

J. C. Doyle, K. Glover, K. Khargonekar, and B. A. Francis, State-space solutions to standard H/sub 2/ and H/sub infinity / control problems, IEEE Transactions on Automatic Control, vol.34, issue.8, pp.831-847, 1989.
DOI : 10.1109/9.29425

J. Doyle, K. Zhou, K. Glover, and B. Bodenheimer, Mixed ???/sub 2/ and ???/sub ???/ performance objectives. II. Optimal control, IEEE Transactions on Automatic Control, vol.39, issue.8, pp.1575-1587, 1994.
DOI : 10.1109/9.310031

L. Elghaoui and V. Nalakrishnan, Synthesis of fixed-structure controllers via numerical optimization, Proceedings of the Conference on Decision and Control, 1994.

L. Ghaoui, F. Oustry, and M. Aitrami, A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE Transactions on Automatic Control, vol.42, issue.8, 1997.

L. Ghaoui and S. Niculescu, Advances in linear matrix inequality methods in control, SIAM advances in design and control, 2000.
DOI : 10.1137/1.9780898719833

B. Farès, P. Apkarian, and D. Noll, An augmented Lagrangian method for a class of LMI-constrained problems in robust control theory, International Journal of Control, vol.74, issue.4, pp.348-360, 2001.
DOI : 10.1080/00207170010010605

B. Farès, D. Noll, and P. Apkarian, Robust Control via Sequential Semidefinite Programming, SIAM Journal on Control and Optimization, vol.40, issue.6, pp.1791-1820, 2002.
DOI : 10.1137/S0363012900373483

E. Feron, P. Apkarian, and P. Gahinet, Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions, IEEE Transactions on Automatic Control, vol.41, issue.7, pp.1041-1046, 1996.
DOI : 10.1109/9.508913

A. V. Fiacco and G. P. Mccormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, 1968.
DOI : 10.1137/1.9781611971316

C. A. Floudas and V. Visweswaran, A global optimization algorithm (GOP) for certain classes of nonconvex NLPs???I. Theory, Computers & Chemical Engineering, vol.14, issue.12, pp.1397-1417, 1990.
DOI : 10.1016/0098-1354(90)80020-C

A. L. Fradkov, Duality theorems for certain nonconvex extremal problems, Siberian Mathematical Journal, vol.9, issue.No. 1, pp.247-264, 1973.
DOI : 10.1007/BF00967951

A. L. Fradkov and V. A. Yakubovich, The S-Procedure and a duality relations in nonconvex problems of quadratic programming, Vestnik Leningrad Univ. Math, vol.6, pp.101-109, 1979.

B. A. Francis, A course in H ? control theory, Lecture Notes in Control and Information Sciences, vol.88, 1987.
DOI : 10.1007/BFb0007371

P. Gahinet and P. Apkarian, A linear matrix inequality approach toH??? control, International Journal of Robust and Nonlinear Control, vol.29, issue.4, pp.421-448, 1994.
DOI : 10.1002/rnc.4590040403

P. Gahinet, P. Apkarian, and M. Chilali, Affine parameter-dependent Lyapunov functions and real parametric uncertainty, IEEE Transactions on Automatic Control, vol.41, issue.3, pp.436-442, 1996.
DOI : 10.1109/9.486646

A. M. Geoffrion, Generalized Benders decomposition, Journal of Optimization Theory and Applications, vol.10, issue.4, 1972.
DOI : 10.1007/BF00934810

J. C. Geromel, P. L. Peres, and J. Bernussou, On a Convex Parameter Space Method for Linear Control Design of Uncertain Systems, SIAM Journal on Control and Optimization, vol.29, issue.2, pp.381-402, 1991.
DOI : 10.1137/0329021

J. C. Geromel, P. L. Peres, and S. R. De-souza, Convex analysis of output feedback control problems: robust stability and performance, IEEE Transactions on Automatic Control, vol.41, issue.7, pp.997-1003, 1997.
DOI : 10.1109/9.508904

J. C. Geromel, C. C. De-souza, and R. E. Skelton, Static output feedback controllers: stability and convexity, IEEE Transactions on Automatic Control, vol.43, issue.1, pp.120-125, 1998.
DOI : 10.1109/9.654912

J. C. Geromel, M. C. De-oliveira, and L. Hsu, LMI characterization of structural and robust stability, Linear Algebra and its Applications, vol.285, issue.1-3, pp.69-80, 1998.
DOI : 10.1016/S0024-3795(98)10123-4

J. C. Geromel, J. Bernussou, and M. C. De-oliveira, H/sub 2/-norm optimization with constrained dynamic output feedback controllers: decentralized and reliable control, IEEE Transactions on Automatic Control, vol.44, issue.7, pp.1449-1454, 1999.
DOI : 10.1109/9.774121

K. Glover, -error bounds???, International Journal of Control, vol.127, issue.6, pp.1115-1193, 1984.
DOI : 10.1109/TIT.1961.1057636

URL : https://hal.archives-ouvertes.fr/in2p3-00956389

K. Goh and M. G. Safonov, Robust analysis, sectors and quadratic functionals, Proceedings of the Conference on Decision and Control, 1995.

K. Goh, M. G. Safonov, and G. P. Papavaissilopoulos, Global optimization for the Biaffine Matrix Inequality problem, Journal of Global Optimization, vol.24, issue.4, pp.365-380, 1995.
DOI : 10.1007/BF01099648

K. Goh, Structure and factorization of quadratic constraints for robustness analysis, Proceddings of the Conference on Decision and Control, 1996.

M. X. Goemans and D. P. Williamson, 878-approximation algorithms for MAX-CUT and MAX-2SAT, Proceedings of the 26th Annual Symposium on Theory of Computing, pp.422-431, 1994.

J. L. Goffin and J. P. Vial, Convex nondifferentiable optimization: A survey focused on the analytic center cutting plane method, Optimization Methods and Software, vol.78, issue.4, p.2, 1999.
DOI : 10.1080/1055678021000060829a

K. M. Grigoriadis and R. E. Skelton, Low-order control design for LMI problems using alternating projection methods, Automatica, vol.32, issue.8, pp.1117-1125, 1996.
DOI : 10.1016/0005-1098(96)00057-X

S. Gugercin and A. C. Antoulas, On consistency and model validation for systems with parametric uncertainty, Proceedings of IFAC Symposium on System Identification, 2000.

S. Gugercin, A. C. Antoulas, and H. P. Zhang, An approach to identification for robust control, IEEE Transactions on Automatic Control, vol.48, issue.6, 2003.
DOI : 10.1109/TAC.2003.812821

B. Halder, B. Hassibi, and T. Kailath, Design of optimal mixed H 2 /H ? static state feedback controllers, Proceeding of the American Control Conference, pp.3239-3243, 1998.

B. Halder and T. Kailath, LMI based design of mixed H 2 /H ? controllers: the state feedback case A spectral bundle method for semidefinite programming, Proceeding of the American Control Conference, pp.1866-1870, 1999.

D. Henrion, S. Tarbouriech, and D. Arzelier, LMI Approximations for the Radius of the Intersection of Ellipsoids: Survey, Journal of Optimization Theory and Applications, vol.72, issue.1, pp.1-28, 2001.
DOI : 10.1023/A:1026454804250

D. Henrion and G. Meinsma, Rank-one LMIs and Lyapunov's inequality, IEEE Transactions on Automatic Control, vol.46, issue.8, pp.1285-1288, 2001.
DOI : 10.1109/9.940935

D. Henrion and J. B. Lasserre, GloptiPoly, Proceedings of the IEEE Conference on Decision and Control, 2002.
DOI : 10.1145/779359.779363

URL : https://hal.archives-ouvertes.fr/hal-00578944

D. Henrion and J. B. Lasserre, GloptiPoly, ACM Transactions on Mathematical Software, vol.29, issue.2, pp.165-194, 2003.
DOI : 10.1145/779359.779363

URL : https://hal.archives-ouvertes.fr/hal-00578944

D. Henrion and J. B. Lasserre, Convergent LMI relaxations for non convex optimization over polynomials in control, IEEE Control Systems Magazine, vol.24, issue.3, 2004.

A. Hiret, C. Valentin-charbonnel, G. Duc, and J. P. Bonnet, Different multidimensional reduction algorithms for the LFT model of a missile, 1998.

J. B. Hiriart-urruty and C. , Convex Analysis and Minimization Algorithms I,II, 1991.
DOI : 10.1007/978-3-662-06409-2

J. B. Hiriart-urruty and M. Torki, Permanently Going Back and Forth between the ``Quadratic World'' and the ``Convexity World'' in Optimization, Applied Mathematics and Optimization, vol.45, issue.2, pp.169-184, 2002.
DOI : 10.1007/s00245-001-0034-6

H. P. Horisberger and P. R. Bélanger, Regulators for linear, time invariant plants with uncertain parameters, IEEE Transactions on Automatic Control, vol.21, issue.5, pp.705-708, 1976.
DOI : 10.1109/TAC.1976.1101350

R. Horst and H. Tuy, Global Optimization: Deterministic Approaches, 1996.

T. Iwasaki, R. E. Skelton, and J. C. , Linear quadratic suboptimal control with static output feedback, Systems & Control Letters, vol.23, issue.6, pp.421-430, 1994.
DOI : 10.1016/0167-6911(94)90096-5

T. Iwasaki and R. E. Skelton, Parametrization of all stabilizing controllers via quadratic Lyapunov functions, Journal of Optimization Theory and Applications, vol.29, issue.No. 2, pp.291-307, 1995.
DOI : 10.1007/BF02192228

T. Iwasaki and R. E. Skelton, -centring algorithm for the dual LMI problem: a new approach to fixed-order control design, International Journal of Control, vol.62, issue.6, pp.1257-1272, 1995.
DOI : 10.1016/0005-1098(93)90130-L

URL : https://hal.archives-ouvertes.fr/hal-00807794

T. Iwasaki and S. Hara, Well-posedness of feedback systems: insights into exact robustness analysis and approximate computations, IEEE Transactions on Automatic Control, vol.43, issue.5, pp.619-630, 1998.
DOI : 10.1109/9.668829

F. Jarre, An interior method for nonconvex semidefinite programs, Optimization and Engineering, vol.1, issue.4, pp.347-372, 2000.
DOI : 10.1023/A:1011562523132

C. Y. Kao and A. Megretski, A new barrier function for IQC optimization problems, Proceedings of the 2003 American Control Conference, 2003., 2003.
DOI : 10.1109/ACC.2003.1240509

J. E. Kelley, The cutting plane method for solving convex programs, Journal of the SIAM, vol.8, pp.703-712, 1960.

P. P. Khargonekar, I. R. Petersen, and K. Zhou, Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory, IEEE Transactions on Automatic Control, vol.35, issue.3, pp.356-361, 1990.
DOI : 10.1109/9.50357

P. Khargonekar and M. Rotea, Mixed H 2 /H ? control: A convex optimization approach, IEEE Transactions on Automatic Control, vol.36, issue.7, pp.823-837, 1991.

V. L. Kharitonov, Asymptotic stability of an equilibrium position of a family of systems of linear differantial equations, Differential'nye Uravneniya, pp.1483-1485, 1978.

M. Ko?vara and M. Stingl, PENNON -A generalized augmented Lagrangian method for semidefinite programming " , Workshop on semidefinite programming and its applications in control theory, combinatorial and global optimization, LAAS-CNRS, 2002.

M. Ko?vara and M. Stingl, PENNON: A code for convex nonlinear and semidefinite programming, Optimization Methods and Software, vol.18, issue.3, pp.317-333, 2003.
DOI : 10.1080/1055678031000098773

J. B. Lasserre, Global Optimization with Polynomials and the Problem of Moments, SIAM Journal on Optimization, vol.11, issue.3, pp.796-817, 2001.
DOI : 10.1137/S1052623400366802

M. Laurent, A Comparison of the Sherali-Adams, Lov??sz-Schrijver, and Lasserre Relaxations for 0???1 Programming, Mathematics of Operations Research, vol.28, issue.3, pp.470-496, 2003.
DOI : 10.1287/moor.28.3.470.16391

M. A. Leal and J. S. Gibson, A first-order Lyapunov robustness method for linear systems with uncertain parameters, IEEE Transactions on Automatic Control, vol.35, issue.9, pp.1068-1070, 1990.
DOI : 10.1109/9.58540

F. Leibfritz, Computational design of stabilizing static output feedback controllers, pp.99-100, 1999.

]. F. Leibfritz and E. M. Mostafa, Optimal static output feedback design by using a trust region interior point method, pp.0-03, 2000.

F. Leibfritz, An LMI-Based Algorithm for Designing Suboptimal Static $\cal H_2/\cal H_\infty$ Output Feedback Controllers, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1711-1735, 2001.
DOI : 10.1137/S0363012999349553

F. Leibfritz and E. M. Mostafa, Trust region methods for solving the optimal output feedback design problem, International Journal of Control, vol.6, issue.5, pp.501-519, 2003.
DOI : 10.1080/02331939008843578

V. J. Leite and P. L. Peres, An Improved LMI condition for robust D-stability of uncertain polytopic systems, IEEE Transactions on Automatic Control, vol.48, issue.3, 2003.

C. Lemarechal, A. Nemirovskii, and Y. Nesterov, New variants of bundle methods, Mathematical Programming, vol.3, issue.1-3, pp.111-147, 1995.
DOI : 10.1007/BF01585555

URL : https://hal.archives-ouvertes.fr/inria-00075054

C. Lemaréchal and F. Oustry, Semidefinite relaxations and Lagrangian duality with applications to combinatorial optimization, 1999.

C. Lemaréchal and A. Renaud, A geometric study of duality gaps, with applications, Mathematical Programming, vol.90, issue.3, pp.399-427, 2001.
DOI : 10.1007/PL00011429

W. Levine and M. Athans, On the determination of the optimal constant output feedback gains for linear multivariable systems, IEEE Transactions on Automatic Control, vol.15, issue.1, pp.44-48, 1970.
DOI : 10.1109/TAC.1970.1099363

J. L. Lin, I. Postlethwaite, and D. W. Gu, ??-K iteration: A new algorithm for ??-synthesis, Automatica, vol.29, issue.1, pp.219-224, 1993.
DOI : 10.1016/0005-1098(93)90185-V

A. I. Lur-'e and V. N. Postnikov, Concerning the theory of stability of regulating systems, Prikl. Mat. Meh, vol.8, pp.246-248, 1944.

P. M. Mäkilä and H. T. Toivonen, Computational methods for parametric LQ problems--A survey, IEEE Transactions on Automatic Control, vol.32, issue.8, pp.658-671, 1987.
DOI : 10.1109/TAC.1987.1104686

O. L. Mangasarian and J. S. Pang, The Extended Linear Complementarity Problem, SIAM Journal on Matrix Analysis and Applications, vol.16, issue.2, pp.359-368, 1995.
DOI : 10.1137/S0895479893262734

I. Masubuchi, A. Ohara, and N. Suda, LMI-based controller synthesis: a unified formulation and solution, International Journal of Robust and Nonlinear Control, vol.8, issue.8, pp.669-686, 1998.
DOI : 10.1002/(SICI)1099-1239(19980715)8:8<669::AID-RNC337>3.0.CO;2-W

A. Megretski, On the order of optimal controllers in the mixed H-2/H-infinity control, Proceedings of 1994 33rd IEEE Conference on Decision and Control, pp.3173-3174, 1994.
DOI : 10.1109/CDC.1994.411627

A. Megretski and A. Rantzer, System analysis via integral quadratic constraints, IEEE Transactions on Automatic Control, vol.42, issue.6, pp.819-830, 1997.
DOI : 10.1109/9.587335

A. M. Meilakhs, Stabilization of linear controlled systems under uncertainty conditions, pp.182-184, 1975.

A. M. Meilakhs, Design of stable control systems subject to parametric perturbation, pp.5-16, 1978.

M. Mesbahi and G. P. Papavassilopoulos, On the rank minimization problem over a positive semidefinite linear matrix inequality, IEEE Transactions on Automatic Control, vol.42, issue.2, pp.239-243, 1997.
DOI : 10.1109/9.554402

M. Mesbahi, On the rank minimization problem and its control applications, Systems & Control Letters, vol.33, issue.1, pp.31-36, 1998.
DOI : 10.1016/S0167-6911(97)00111-4

M. Mesbahi, A semi-definite programming solution of the least order dynamic output feedback synthesis problem, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), pp.2355-2359, 1999.
DOI : 10.1109/CDC.1999.830903

T. Mori and H. Kokame, A parmater-dependent Lyapunov function for a polytope of matrices, IEEE Transactions on Automatic Control, vol.45, issue.8, 2000.

D. Mustafa, Relations between maximum-entropy/H??? control and combined H???/LQG control, Systems & Control Letters, vol.12, issue.3, pp.193-203, 1989.
DOI : 10.1016/0167-6911(89)90050-9

Y. Nesterov and A. Nemirovskii, Interior-point polynomial algorithms in convex programming , SIAM Studies in applied mathematics, 1994.

Y. Nesterov, H. Frenk, K. Roos, and T. Terlaky, Squared Functional Systems and Optimization Problems, High performance optimization, 2000.
DOI : 10.1007/978-1-4757-3216-0_17

A. Neumaier, Complete search in continuous global optimization and constraint satisfaction, Acta Numerica, 2004.

D. Noll, M. Torki, and P. Apkarian, Partially Augmented Lagrangian Method for Matrix Inequality Constraints, SIAM Journal on Optimization, vol.15, issue.1
DOI : 10.1137/S1052623402413963

M. C. De-oliveira and J. C. , Numerical comparison of output feedback design methods, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041), 1997.
DOI : 10.1109/ACC.1997.611757

A. Packard and J. C. Doyle, Quadratic stability with real and complex perturbations, IEEE Transactions on Automatic Control, vol.35, issue.2, pp.198-201, 1990.
DOI : 10.1109/9.45179

A. Packard and J. Doyle, The complex structured singular value Higher order semidefinite relaxations for quadratic programming, Proceedings of the 39th IEEE Conference on Decision and Control, pp.71-109, 1993.

P. Parrilo, Semidefinite programming relaxations for semialgebraic problems, Mathematical Programming, vol.96, issue.2, pp.293-320, 2003.
DOI : 10.1007/s10107-003-0387-5

P. Parrilo, Semidefinite Programming Relaxations and Algebraic Optimization in Control, European Journal of Control, vol.9, issue.2-3, pp.301-321, 2003.
DOI : 10.3166/ejc.9.307-321

D. Peaucelle, Formulation générique deprobì emes en analyse et commande robuste par les fonctions de Lyapunov dépendant des paramètres, Thèse de Doctorat en Automatique, 2000.

D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou, A new robust -stability condition for real convex polytopic uncertainty, Systems & Control Letters, vol.40, issue.1, 2000.
DOI : 10.1016/S0167-6911(99)00119-X

D. Peaucelle and D. Arzelier, Robust performance analysis with LMI-based methods for real parametric uncertainty via parameter-dependent Lyapunov functions, IEEE Transactions on Automatic Control, vol.46, issue.4, pp.624-630, 2001.
DOI : 10.1109/9.917664

D. Peaucelle and D. Arzelier, Efficient numerical solutions for H 2 static output feedback synthesis, Proceedings of the European Control Conference, 2001.

D. Peaucelle and D. Arzelier, ELLIPSOIDAL SETS FOR STATIC OUTPUT FEEDBACK, Proceedings of the Automatic Control 15th IFAC World Congress, 2002.
DOI : 10.3182/20020721-6-ES-1901.00195

P. L. Peres, J. C. Geromel, and A. M. Almulgla, Quadratic stabilizability of linear uncertain systems, Proceedings of the European Control Conference, 1993.

B. T. Polyak, Convexity of Quadratic Transformations and Its Use in Control and Optimization, Journal of Optimization Theory and Applications, vol.6, issue.3, pp.553-583, 1998.
DOI : 10.1023/A:1021798932766

S. Prajna, A. Papachristodolou, and P. Parillo, SOSTOOLS: Sum of squares optimization toolbox for MATLAB " , disponible sur le site http, 2002.

P. Psarris and C. A. Floudas, Robust stability analysis of systems with real parametric uncertainty: A global optimization approach, International Journal of Robust and Nonlinear Control, vol.3, issue.8, pp.699-717, 1995.
DOI : 10.1002/rnc.4590050803

E. S. Pyatniskii and V. I. Skorindiskii, Numerical methods of Lyapunov function construction and their application to the absolute stability problem, Systems & Control Letters, vol.2, issue.2, pp.130-135, 1982.
DOI : 10.1016/S0167-6911(82)80023-6

D. C. Ramos and P. L. Peres, An LMI condition for the robust stability of uncertain continuous-time linear systems, IEEE Transactions on Automatic Control, vol.47, issue.4, pp.675-678, 2002.
DOI : 10.1109/9.995048

R. M. Redheffer, On a Certain Linear Fractional Transformation, Journal of Mathematics and Physics, vol.65, issue.1-4, pp.269-286, 1960.
DOI : 10.1002/sapm1960391269

D. B. Ridgely, C. P. Mracek, and L. Valavani, Numerical solutions of the general mixed H 2 /H ? optimization problem, Proceeding of the American Control Conference, pp.1353-1357, 1992.

D. B. Ridgely, L. Valavani, M. Dahleh, and G. Stein, Solution to the general mixed H 2 /H ? control problem -necessary conditions for optimality, Proceeding of the American Control Conference, pp.1348-1352, 1992.

J. Rohn, Systems of linear interval equations, Linear Algebra and its Applications, vol.126, pp.39-78, 1989.
DOI : 10.1016/0024-3795(89)90004-9

M. Rotea and P. Khargonekar, H2-optimal control with an H???-constraint The state feedback case, Automatica, vol.27, issue.2, pp.307-316, 1991.
DOI : 10.1016/0005-1098(91)90079-H

M. Rotea and T. Iwasaki, An alternative to the D-K iteration?, Proceedings of 1994 American Control Conference, ACC '94, pp.53-57, 1993.
DOI : 10.1109/ACC.1994.751692

M. G. Safonov, L ? optimal sensitivity against stability margin, Proceedings of the Conference on Decision and Control, 1983.
DOI : 10.1109/cdc.1983.269807

M. G. Safonov, Stability and Robustness of Multivariable Feedback Systems, 1980.

C. Scherer, P. Gahinet, and M. Chilali, Multiobjective output-feedback control via LMI optimization, IEEE Transactions on Automatic Control, vol.42, issue.7, pp.896-911, 1997.
DOI : 10.1109/9.599969

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.5458

C. W. Scherer, A full block S-procedure with applications, Proceedings of the 36th IEEE Conference on Decision and Control, pp.2602-2607, 1997.
DOI : 10.1109/CDC.1997.657769

G. Scorletti and L. Elghaoui, Improved LMI conditions for gain scheduling and related control problems, International Journal of Robust and Nonlinear Control, vol.8, issue.10, pp.845-877, 1998.
DOI : 10.1002/(SICI)1099-1239(199808)8:10<845::AID-RNC350>3.0.CO;2-I

Z. Shi and W. Gao, A necessary and sufficient condition for the positive-definiteness of interval symmetric matrices, International Journal of Control, vol.43, issue.1, pp.325-328, 1986.
DOI : 10.1080/00207178408933211

N. Shor, Minimization Methods for Non-differentiable Functions Quadratic optimization problems, Soviet J. Circuits Systems Sci, vol.25, pp.1-11, 1985.
DOI : 10.1007/978-3-642-82118-9

N. Shor, Nondifferential Optimization and Polynomial Problems, 1998.

R. E. Skelton and T. Iwasaki, Increased roles of linear algebra in control education, IEEE Control Systems, vol.15, issue.4, pp.76-90, 1995.
DOI : 10.1109/37.408458

R. E. Skelton, T. Iwasaki, and K. Grigoriadis, A unified algebraic approach top linear control design, 1998.

V. L. Syrmos, C. T. Abdallah, P. Dorato, and K. Grigoriadis, Static output feedback???A survey, Automatica, vol.33, issue.2, pp.125-137, 1997.
DOI : 10.1016/S0005-1098(96)00141-0

]. O. Toker and H. Ozbay, On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback, Proceedings of 1995 American Control Conference, ACC'95, pp.2056-2064, 1995.
DOI : 10.1109/ACC.1995.532300

P. Tseng, Dual coordinate ascent methods for non-strictly convex minimization, Mathematical Programming, vol.28, issue.1-3, pp.231-247, 1993.
DOI : 10.1007/BF01581245

P. Tseng, Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization, Journal of Optimization Theory and Applications, vol.109, issue.3, pp.475-494, 2001.
DOI : 10.1023/A:1017501703105

H. Tuy, Convex Analysis and Global Optimization, 1998.

L. Vandenberghe and V. Balakrishnan, Semidefinite Programming, SIAM Review, vol.38, issue.1, pp.49-95, 1996.
DOI : 10.1137/1038003

D. Walker and B. Ridgely, Uniqueness of the general mixed H 2 /H ? optimal controller, Proceedings of the American Control Conference, pp.1453-1457, 1995.

M. R. Waszak and D. Andrisani, Uncertainty modeling via frequency domain model validation, Guidance, Navigation, and Control Conference and Exhibit, 1999.
DOI : 10.2514/6.1999-3959

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.45.4690

S. R. Wells and D. B. Ridgely, Using increased order controllers in mixed H 2 /H ? optimization, Proceedings of the American Control Conference, 1992.

J. C. Willems, Least squares stationary optimal control and the algebraic Riccati equation, IEEE Transactions on Automatic Control, vol.16, issue.6, pp.621-634, 1971.
DOI : 10.1109/TAC.1971.1099831

H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook of semidefinite programming, Kluwer's international series, 2000.

V. A. Yakubovich, S-procedure in nonlinear control theory, Vestnik Leningrad Univ, vol.1, pp.62-77, 1971.

V. A. Yakubovich, Minimization of quadratic functionals under quadratic constraints and the necessity of a frequency condition in the quadratic criterion for absolute stability of nonlinear control systems, Soviet Math. Dokl, vol.14, issue.2, pp.593-597, 1973.

V. A. Yakubovich, Nonconvex optimization problem: The infinite-horizon linear-quadratic control problem with quadratic constraints, Systems & Control Letters, vol.19, issue.1, pp.13-22, 1992.
DOI : 10.1016/0167-6911(92)90034-P

R. K. Yedavalli, A necessary and sufficient extreme point solution for checking robust stability of polytopes of matrices, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000.
DOI : 10.1109/ACC.2000.879516

H. H. Yeh and S. S. Banda, Necessary and sufficient conditions for mixed H/sub 2/ and H/sub infinity / optimal control, IEEE Transactions on Automatic Control, vol.37, issue.3, pp.355-358, 1992.
DOI : 10.1109/9.119636

P. M. Young, Controller design with mixed uncertainties, Proceedings of 1994 American Control Conference, ACC '94, pp.2333-2337, 1994.
DOI : 10.1109/ACC.1994.752496

G. Zames, Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses, IEEE Transactions on Automatic Control, vol.26, issue.2, pp.301-320, 1981.
DOI : 10.1109/TAC.1981.1102603

G. Zames and B. A. Francis, Feedback, minimax sensitivity, and optimal robustness, IEEE Transactions on Automatic Control, vol.28, issue.5, pp.585-601, 1983.
DOI : 10.1109/TAC.1983.1103275

L. Méthodes-de-pénalité-et-debarrì-ere and .. , 43 1.6.3 L'optimisation non différentiable, p.47

.. La-synthèse-par-retour-de-sortie-statique, 67 3.1.1 Introduction, 67 3.1.2 Formulation duprobì eme et hypothèses . . . . . . . . . . . . . . . . 67