équilibre stable et l'ensemble (discret) des équilibres instables en boucle fermée, l'attribut « presque »provient du fait que (a) il n'existe pas d'ensemble M dense pour lequel toute condition initiale choisie dans M conduit à des trajectoires convergeant vers Q et que (b) ,
Théorie de Lyapunov, commande robuste et optimisation, LAAS-CNRS, 2004. ,
PERIODIC OPERATION OF CHEMICAL REACTORS: A REVIEW, Chemical Engineering Communications, vol.7, issue.43, pp.111-124, 1974. ,
DOI : 10.1080/00986447408960421
A lifting technique for linear periodic systems with applications to sampled-data control, Systems & Control Letters, vol.17, issue.2, pp.79-88, 1991. ,
DOI : 10.1016/0167-6911(91)90033-B
New Tools for Robustness of Linear Systems, 1994. ,
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
A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon, Systems & Control Letters, vol.39, issue.1, pp.63-70, 2000. ,
DOI : 10.1016/S0167-6911(99)00090-0
Analysis of discrete-time linear periodic systems, Control and Dynamic Systems, vol.78, pp.313-339, 1996. ,
DOI : 10.1016/S0090-5267(96)80056-9
A LMI characterization of the class of stabilizing controllers for periodic discretetime systems, 14th IFAC World Congress, 1999. ,
Invariant representations of discrete-time periodic systems, Automatica, vol.36, issue.12, pp.1777-1793, 2000. ,
DOI : 10.1016/S0005-1098(00)00087-X
Periodic Systems : Filtering and Control, 2008. ,
An LMI approach to periodic discrete-time unbiased filtering, Systems & Control Letters, vol.42, issue.1, pp.21-35, 2001. ,
DOI : 10.1016/S0167-6911(00)00075-X
On the Zero Dynamics of Helicopter Rotor Loads, European Journal of Control, vol.2, issue.1, pp.57-68, 1996. ,
DOI : 10.1016/S0947-3580(96)70029-8
Encyclopedia of Electrical and Electronics Engineering, chapter Periodic Control, pp.59-73, 1999. ,
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
An existence result for polynomial solutions of parameter-dependent LMIs, Systems & Control Letters, vol.51, issue.3-4, pp.3-4165, 2004. ,
DOI : 10.1016/j.sysconle.2003.08.001
URL : https://hal.archives-ouvertes.fr/inria-00071788
Nonholonomic mechanics and control, 2003. ,
DOI : 10.1007/b97376
Nonholonomic dynamics, Notices of the AMS, vol.52, issue.3, pp.320-329, 2005. ,
Linear matrix inequalities in system and control theory, Proceedings of the IEEE, vol.85, issue.4, pp.698-699, 1997. ,
DOI : 10.1137/1.9781611970777
A classification of linear controllable systems, Kybernetika, vol.3, issue.6, pp.173-188, 1970. ,
On the attitude stabilization of rigid spacecraft, Automatica, vol.27, issue.1, pp.87-95, 0197. ,
DOI : 10.1016/0005-1098(91)90008-P
Predictive Control using Semi-definite Programming -Efficient Approaches for Periodic Systems and Lur'e Systems, 2011. ,
Orbit-averaged behavior of magnetic control laws for momentum unloading, Journal of Guidance, Control, and Dynamics, vol.3, issue.6, pp.563-568, 1980. ,
DOI : 10.2514/3.19725
Rigid-Body Attitude Control, IEEE Control Systems, vol.31, issue.3, pp.3130-51, 2011. ,
DOI : 10.1109/MCS.2011.940459
Optimal Combined Reaction-Wheel Momentum Management for Earth-Pointing Satellites, Journal of Guidance, Control, and Dynamics, vol.22, issue.4, pp.543-550, 1999. ,
DOI : 10.2514/2.4431
Positive polynomials in control, chapter An LMI-based technique for robust stability analysis of linear systems with polynomial parametric uncertainties, pp.87-101, 2004. ,
Homogeneous Polynomial Forms for Robustness Analysis of Uncertain Systems, 2009. ,
DOI : 10.1007/978-1-84882-781-3
Positive semidefinite biquadratic forms, Linear Algebra and its Applications, vol.12, issue.2, pp.95-100, 1975. ,
DOI : 10.1016/0024-3795(75)90058-0
URL : http://doi.org/10.1016/0024-3795(75)90058-0
Nonlinear control of a swinging pendulum, Automatica, vol.31, issue.6, pp.31851-862, 1995. ,
DOI : 10.1016/0005-1098(94)00148-C
Theoretical aspects of continuous-time periodic systems, Annual Reviews in Control, vol.29, issue.2, pp.205-215, 2005. ,
DOI : 10.1016/j.arcontrol.2005.04.001
Spacecraft attitude dynamics and control in the presence of large magnetic residuals, Control Engineering Practice, vol.17, issue.4, pp.456-68, 2009. ,
DOI : 10.1016/j.conengprac.2008.09.010
Control of Linear Parameter Varying systems with applications, chapter Attitude Regulation for Spacecraft with Magnetic Actuators : An LPV Approach, p.339, 2012. ,
Techniques & technologies des véhicules spatiaux, 1998. ,
Guaranteed cost control of uncertain nonlinear systems via polynomial lyapunov functions, IEEE Transactions on Automatic Control, vol.47, issue.9, pp.1575-1580, 2002. ,
DOI : 10.1109/TAC.2002.802737
Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties, Systems & Control Letters, vol.43, issue.5, pp.355-359, 2001. ,
DOI : 10.1016/S0167-6911(01)00118-9
A new discrete-time robust stability condition, Systems & Control Letters, vol.37, issue.4, pp.261-265, 1999. ,
DOI : 10.1016/S0167-6911(99)00035-3
An LMI approach to stabilization of linear discrete-time periodic systems, International Journal of Control, vol.73, issue.8, pp.696-703, 2000. ,
DOI : 10.1080/002071700403466
Magnetic momentum management for a geostationary satellite platform, IET Control Theory & Applications, vol.3, issue.10, pp.1370-1382, 2009. ,
DOI : 10.1049/iet-cta.2008.0327
New robust stability and performance conditions based on parameter dependent multipliers, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), pp.4187-4192, 2000. ,
DOI : 10.1109/CDC.2001.914554
Review of LFTs, LMIs, and µ, Decision and Control Proceedings of the 30th IEEE Conference on, pp.1227-1232, 1991. ,
Commande H ? et µ-analyse : des outils pour la robustesse, Hermes Science, 1999. ,
Robust performance of periodic systems, IEEE Transactions on Automatic Control, vol.41, issue.8, pp.411146-1159, 1996. ,
DOI : 10.1109/9.533676
A course in robust control theory, 2000. ,
DOI : 10.1007/978-1-4757-3290-0
A new approach for analysis and synthesis of time-varying systems, IEEE Transactions on Automatic Control, vol.44, issue.8, pp.1486-1497, 1999. ,
DOI : 10.1109/9.780413
Robust H<inf>2</inf> control of uncertain discrete-time linear systems with periodically time-varying memory state-feedback, 2010 IEEE International Symposium on Computer-Aided Control System Design, 2012. ,
DOI : 10.1109/CACSD.2010.5612782
LMIs in control, IEEE-CDC and ECC, 2005. ,
Periodically time-varying dynamical controller synthesis for polytopictype uncertain discrete-time linear systems, Proceedings of the 47th IEEE Conference on Decision and Control, pp.5438-5443, 2008. ,
LMI-based Periodically Time-Varying Dynamical Controller Synthesis for Discrete-Time Uncertain Linear Systems, 17th IFAC World Congress, 2008. ,
DOI : 10.3182/20080706-5-KR-1001.00232
Further results on periodically timevarying memory state-feedback controller synthesis for discrete-time linear systems, Proceedings of the 48th IEEE Conference on Decision and Control and Chinese Control Conference, pp.702-707, 2009. ,
DOI : 10.1109/cdc.2009.5399919
Robust Performance Analysis of Uncertain LTI Systems: Dual LMI Approach and Verifications for Exactness, IEEE Transactions on Automatic Control, vol.54, issue.5, pp.938-951, 2009. ,
DOI : 10.1109/TAC.2009.2017086
Analysis of Uncertain Discrete-Time Linear Periodic Systems based on System Lifting and LMIs, European Journal of Control, vol.16, issue.5, pp.532-544, 2010. ,
DOI : 10.3166/ejc.16.532-544
Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems, Automatica, vol.47, issue.1, pp.14-25, 2011. ,
DOI : 10.1016/j.automatica.2010.10.004
Advances in linear matrix inequality methods in control, Society for Industrial Mathematics, 2000. ,
DOI : 10.1137/1.9780898719833
On a Peculiar Class of Acoustical Figures; and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces, Philosophical Transactions of the Royal Society of London, vol.121, issue.0, pp.299-340, 1831. ,
DOI : 10.1098/rstl.1831.0018
Méthodes d'analyse et de synthèse robustes pour les systèmes linéaires périodiques, 2006. ,
Robust H 2 performance analysis and synthesis of linear polytopic discrete-time periodic systems via LMIs. System and Control Letters, pp.159-166, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00168061
Comments on " the attitude control problem " . Automatic Control, IEEE Transactions on, vol.39, issue.3, pp.699-700, 1994. ,
Sur les équations différentielles lineaires à coefficients périodiques. Annales de l'école normale supérieure, pp.47-89, 1883. ,
Geometric Approach to Spacecraft Attitude Control Using Magnetic and Mechanical Actuation, Journal of Guidance, Control, and Dynamics, vol.33, issue.2, pp.590-595, 2010. ,
DOI : 10.2514/1.46441
Periodic motions of the Pendubot via virtual holonomic constraints: Theory and experiments, Automatica, vol.44, issue.3, pp.785-791, 2008. ,
DOI : 10.1016/j.automatica.2007.07.011
Optimal Control Laws for Momentum-Wheel Desaturation Using Magnetorquers, Journal of Guidance, Control, and Dynamics, vol.29, issue.6, pp.1464-1468, 2006. ,
DOI : 10.2514/1.23396
Comparative stability analysis and performance of magnetic controllers for bias momentum satellites, Journal of Guidance, Control, and Dynamics, vol.18, issue.6, pp.1313-1320, 1995. ,
DOI : 10.2514/3.21547
Pole-Placement Technique for Magnetic Momentum Removal of Earth-Pointing Spacecraft, Journal of Guidance, Control, and Dynamics, vol.20, issue.2, pp.268-275, 1997. ,
DOI : 10.2514/2.4062
Nonlinear dynamical systems and control : a Lyapunov-based approach, 2011. ,
On parameter-dependent Lyapunov functions for robust stability of linear systems, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), pp.887-892, 2004. ,
DOI : 10.1109/CDC.2004.1428797
On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon, Acta Mathematica, vol.8, issue.0, pp.1-36, 1886. ,
DOI : 10.1007/BF02417081
Mathematical systems theory I : modelling, state space analysis, stability and robustness, 2005. ,
DOI : 10.1007/b137541
Handbook of linear algebra, 2007. ,
DOI : 10.1201/9781420010572
Periodic Processes: A Variational Approach, Industrial & Engineering Chemistry Process Design and Development, vol.6, issue.1, pp.21-30, 1967. ,
DOI : 10.1021/i260021a005
Properties of discrete-time noncausal linear periodically time-varying scaling and their relationship with shift-invariance in lifting-timing, International Journal of Control, vol.46, issue.6, pp.1067-1079, 2011. ,
DOI : 10.1016/0167-6911(95)00063-1
Spacecraft attitude dynamics, 1986. ,
Robust attitude stabilization of spacecraft using nonlinear quaternion feedback. Automatic Control, IEEE Transactions on, vol.40, issue.10, pp.1800-1803, 1995. ,
Linear systems, 1980. ,
A cutting plane algorithm for robustness analysis of periodically time-varying systems, IEEE Transactions on Automatic Control, vol.46, issue.4, pp.579-592, 2001. ,
DOI : 10.1109/9.917659
Robust controller synthesis for uncertain discrete-time periodic systems, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), pp.3129-3130, 1998. ,
DOI : 10.1109/ACC.1998.688437
Some results about stabilization of periodic takagi-sugeno models, 2009 IEEE International Conference on Fuzzy Systems, pp.814-819, 2009. ,
DOI : 10.1109/FUZZY.2009.5277323
Nonlinear Systems, 2002. ,
Robust control of linear time-invariant plants using periodic compensation, IEEE Transactions on Automatic Control, vol.30, issue.11, pp.1088-1096, 1985. ,
DOI : 10.1109/TAC.1985.1103841
Moments, positive polynomials and their applications, 2010. ,
DOI : 10.1142/p665
Optimal Magnetic Momentum Control for Inertially Pointing Spacecraft, European Journal of Control, vol.7, issue.1, pp.30-39, 2001. ,
DOI : 10.1016/S0947-3580(01)70936-3
Spacecraft attitude control using magnetic actuators, Automatica, issue.8, pp.401405-1414, 2004. ,
DOI : 10.1016/j.automatica.2004.02.022
Periodic attitude control techniques for small satellites with magnetic actuators, IEEE Transactions on Control Systems Technology, vol.10, issue.1, pp.90-95, 2002. ,
DOI : 10.1109/87.974341
Sur une série relative a la théorie des équations différentielles linéaires avec coefficients périodiques, Compte Rendu Acad. Sci. Paris, vol.1232, issue.26, pp.1248-1252, 1956. ,
A nonlinear magnetic controller for three-axis stability of nanosatellites. Master's thesis, Faculty of the Virginia Polytechnic Institute, 2001. ,
Mémoire sur le mouvement vibratoire d'une membrane de forme elliptique, Journal de mathématiques pures et appliquées, pp.137-203, 1868. ,
Robust global asymptotic attitude stabilization of a rigid body by quaternion-based hybrid feedback, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp.2522-2527, 2009. ,
DOI : 10.1109/CDC.2009.5400431
Satellite Angular Momentum Removal Utilizing the Earth's Magnetic Field, Torques and attitude sensing in Earth satellites, pp.137-158, 1964. ,
DOI : 10.1016/B978-0-12-395776-4.50015-X
Jensen's inequality, Bulletin of the American Mathematical Society, vol.43, issue.8, 1937. ,
DOI : 10.1090/S0002-9904-1937-06588-8
Time-varying feedback stabilization of the attitude of a rigid spacecraft with two controls, Systems & Control Letters, vol.25, issue.5, pp.375-385, 1995. ,
DOI : 10.1016/0167-6911(94)00095-D
Periodic-polynomial interpretation for structural properties of linear periodic discrete-time systems, Systems & Control Letters, vol.33, issue.4, pp.241-251, 1998. ,
DOI : 10.1016/S0167-6911(97)00099-6
Interior-point polynomial algorithms in convex programming, SIAM, 1994. ,
DOI : 10.1137/1.9781611970791
Duality for linear time invariant finite dimensional systems, Analysis and Optimization of Systems, pp.11-21, 1988. ,
DOI : 10.1007/BFb0042197
Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations, IEEE Transactions on Automatic Control, vol.52, issue.7, pp.1334-1340, 2007. ,
DOI : 10.1109/TAC.2007.900848
Quadratic stability with real and complex perturbations. Automatic Control, IEEE Transactions on, vol.35, issue.2, pp.198-201, 1990. ,
DOI : 10.1109/9.45179
Formulation générique de problèmes en analyse et commande robuste par les fonctions de Lyapunov dépendant des paramètres, 2000. ,
LMI tests for positive definite polynomials : Slack variable approach. Automatic Control, IEEE Transactions on, vol.54, issue.4, pp.886-891, 2009. ,
DOI : 10.1109/tac.2008.2010971
A new robust -stability condition for real convex polytopic uncertainty, Systems & Control Letters, vol.40, issue.1, pp.21-30, 2000. ,
DOI : 10.1016/S0167-6911(99)00119-X
II, Location of Zeros, Collected Papers, 1974. ,
Magnetic Torquer Attitude Control via Asymptotic Periodic Linear Quadratic Regulation, Journal of Guidance, Control, and Dynamics, vol.24, issue.2, pp.386-94, 2001. ,
DOI : 10.2514/2.4723
Advanced techniques for satellites modeling and attitude control, 2008. ,
Optimal Discrete-Time Design of Three-Axis Magnetic Attitude Control Laws, IEEE Transactions on Control Systems Technology, vol.18, issue.3, pp.714-722, 2010. ,
DOI : 10.1109/TCST.2009.2024757
Systems with structured uncertainty : Relations between quadratic and robust stability. Automatic Control, IEEE Transactions on, vol.38, issue.5, pp.799-803, 1993. ,
DOI : 10.1109/9.277250
Duality in time-varying linear systems : a module theoretic approach. Linear algebra and its applications, pp.83-106, 1996. ,
Concerning adjoints of discrete-time systems, IEEE Transactions on Automatic Control, vol.10, issue.3, pp.350-352, 1965. ,
DOI : 10.1109/TAC.1965.1098139
Analytical Mechanics of Space Systems, 2003. ,
DOI : 10.2514/4.861550
LMI Relaxations in Robust Control, European Journal of Control, vol.12, issue.1, pp.3-29, 2006. ,
DOI : 10.3166/ejc.12.3-29
Matrix Sum-of-Squares Relaxations for Robust Semi-Definite Programs, Mathematical Programming, vol.107, issue.1-2, pp.189-211, 2006. ,
DOI : 10.1007/s10107-005-0684-2
Relaxations for Robust Linear Matrix Inequality Problems with Verifications for Exactness, SIAM Journal on Matrix Analysis and Applications, vol.27, issue.2, pp.365-395, 2005. ,
DOI : 10.1137/S0895479803430953
Spacecraft dynamics and control : a practical engineering approach, 1997. ,
DOI : 10.1017/CBO9780511815652
A Unified Algebraic Approach to Linear Control Design, 1997. ,
Remarks on stabilization and input-to-state stability, Proceedings of the 28th IEEE Conference on Decision and Control, pp.1376-1378, 1989. ,
DOI : 10.1109/CDC.1989.70365
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.4748
An elementary magnetic attitude control system, American Institute of Aeronautics and Astronautics, Mechanics and Control of Flight Conference, 1974. ,
Full-State Feedback Control of a Variable-Speed Wind Turbine: A Comparison of Periodic and Constant Gains, Journal of Solar Energy Engineering, vol.123, issue.4, pp.319-326, 2001. ,
DOI : 10.1115/1.1412237
Periodic FIR controller synthesis for discrete-time uncertain linear systems, IEEE Conference on Decision and Control and European Control Conference, pp.1367-1372, 2011. ,
DOI : 10.1109/CDC.2011.6161068
Periodic H<inf>2</inf> synthesis for spacecraft attitude control with magnetorquers and reaction wheels, IEEE Conference on Decision and Control and European Control Conference, pp.6876-6881, 2011. ,
DOI : 10.1109/CDC.2011.6161179
Contrôle d'attitude périodique avec magnéto-coupleurs et roues à réactions, Journées Nationales MACS, 2011. ,
Robust H ? performance of periodic systems with memory : New formulations, analysis and design results, Proceedings of the 51th IEEE Conference on Decision and Control, 2012. ,
Robust stability of periodic systems with memory : New formulations, analysis and design results, Proceedings of the 7th IFAC Symposium on Robust Control Design, 2012. ,
Periodic Memory State-Feedback Controller: New Formulation, Analysis, and Design Results, IEEE Transactions on Automatic Control, vol.58, issue.8, 2012. ,
DOI : 10.1109/TAC.2013.2251820
Fundamentals of astrodynamics and applications, 2001. ,
Analysis of Controlled Dynamical Systems, chapter Duality for linear systems : External and state space characterization of the adjoint system, pp.393-403, 1991. ,
Decomposition techniques for large-scale systems with nonadditive interactions: Stability and stabilizability, IEEE Transactions on Automatic Control, vol.25, issue.4, pp.773-779, 1980. ,
DOI : 10.1109/TAC.1980.1102422
The attitude control problem, IEEE Transactions on Automatic Control, vol.36, issue.10, pp.1148-1162, 1991. ,
DOI : 10.1109/9.90228
Spacecraft attitude determination and control, 1978. ,
DOI : 10.1007/978-94-009-9907-7
Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2003. ,
DOI : 10.1007/978-1-4757-4067-7
Fully magnetic attitude control for spacecraft subject to gravity gradient, Automatica, vol.35, issue.7, pp.1201-1214, 1999. ,
DOI : 10.1016/S0005-1098(99)00021-7
Generalized H 2 control synthesis for periodic systems, Proceedings of the IEEE American Control Conference, pp.25-27, 2001. ,
Periodic H2 Synthesis for Spacecraft Attitude Control with Magnetorquers, Journal of Guidance, Control, and Dynamics, vol.27, issue.5, pp.696-709, 2004. ,
DOI : 10.2514/1.10457
On dynamic control allocation for input-redundant control systems, 2007 46th IEEE Conference on Decision and Control, pp.1431-1438, 2009. ,
DOI : 10.1109/CDC.2007.4434679
H??? attitude control of magnetically actuated satellites*, IFAC World Congress, pp.8479-8484, 2011. ,
DOI : 10.3182/20110828-6-IT-1002.02751
Essentials of robust control, NJ, vol.104, 1998. ,