Linear stability analysis of self-excited vibrations in drilling using an infinite dimensional model, Journal of Sound and Vibration, vol.360, pp.239-259, 2016. ,
Torsional vibrations with bit off bottom: Modeling, characterization and field data validation, Journal of Petroleum Science and Engineering, vol.163, pp.712-721, 2018. ,
Dissipation inequalities for the analysis of a class of PDEs, Automatica, vol.66, pp.163-171, 2016. ,
Stability analysis of time-varying delay systems in quadratic separation framework, ICNPAA-2008: Mathematical Problems in Engineering, Aerospace and Sciences, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00357766
Stability analysis of timedelay systems via Bessel inequality: A quadratic separation approach, International Journal of Robust and Nonlinear Control, vol.28, issue.5, pp.1507-1527, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01699172
Stick-slip arising from stribeck friction, Proceedings., IEEE International Conference on Robotics and Automation, pp.1377-1382, 1990. ,
A survey of models, analysis tools and compensation methods for the control of machines with friction, Automatica, vol.30, issue.7, pp.1083-1138, 1994. ,
Nonlinear control engineering-describing function analysis and design, IEEE Transactions on Systems, Man, and Cybernetics, vol.7, issue.9, pp.678-678, 1977. ,
Robust design of backstepping controllers for systems of linear-hyperbolic PDEs. Theses, 2018. ,
Drilling engineering. PennWell books, 2007. ,
Stabilité et stabilisation de systèmes linéairesà l'aide d'inégalités matricielles linéaires. Quadrature, 2019. ,
Static state and output feedback synthesis for time-delay systems, European Control Conference (ECC), pp.1195-1200, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01639829
Pratical stability of a drilling pipe under friction with a pi-controller, IEEE Transaction on Control Systems Technologies, 2019. ,
Input/output stability of a damped string equation coupled with ordinary differential system, International Journal of Robust and Nonlinear Control, vol.28, issue.18, pp.6053-6069, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01690626
Wirtinger-based exponential stability for time-delay systems, IFAC World Congress, vol.50, pp.11984-11989, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01488920
Exponential Lyapunov stability analysis of a drilling mechanism, 57th Annual Conference on Decision and Control (CDC), pp.2952-2957, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01725416
Stabilization of an unstable wave equation using an infinite dimensional dynamic controller, 57th Annual Conference on Decision and Control (CDC), pp.2952-2957, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01845845
Lyapunov stability of a coupled ordinary differential system and a string equation with polytopic uncertainties, Advances on Delays and Dynamics, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01796803
Lyapunov stability analysis of a string equation coupled with an ordinary differential system, IEEE Transactions on Automatic Control, vol.63, issue.11, pp.3850-3857, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01548256
Stability and boundary stabilization of 1-d hyperbolic systems, vol.88, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01449504
Observer-based boundary control design for the suppression of stickslip oscillations in drilling systems with only surface measurements, Journal of Dynamic Systems, Measurement, and Control, vol.139, issue.10, p.104501, 2017. ,
Differential-difference equations, 1963. ,
Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM Journal on Mathematical Analysis, vol.33, issue.5, pp.1144-1165, 2002. ,
Linear Matrix Inequalities in System and Control Theory, Studies in Applied Mathematics. SIAM, 1994. ,
Pseudospectral differencing methods for characteristic roots of delay differential equations, SIAM Journal on Scientific Computing, vol.27, issue.2, pp.482-495, 2005. ,
Adaptive output feedback for oil drilling stick-slip instability modeled by wave PDE with anti-damped dynamic boundary, ACC, pp.386-391, 2014. ,
Output-feedback adaptive control of a wave PDE with boundary anti-damping, Automatica, vol.50, issue.5, pp.1407-1415, 2014. ,
Functional analysis, Sobolev spaces and partial differential equations, 2010. ,
Convergence and equivalence results for the Jensen's inequality -application to time-delay and sampled-data systems, IEEE Transactions on Automatic Control, vol.56, issue.7, pp.1660-1665, 2011. ,
Linear parameter-varying and time-delay systems. Analysis, observation, filtering & control, vol.3, 2014. ,
Robust stability of impulsive systems: A functional-based approach, 4th IFAC conference on Analysis and Design of Hybrid Systems (ADHS'2012), p.6, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00679207
DOSKIL: A New Mechanism for Controlling Stick-Slip Oscillations in Oil Well Drillstrings, IEEE Transactions on Control Systems Technology, vol.16, issue.6, pp.1177-1191, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00394990
Dynamic Boundary Stabilization of Linear and Quasi-Linear Hyperbolic Systems, 51st Annual Conference on Decision and Control (CDC), pp.2952-2957, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00718725
Effect of time scales on stability of coupled systems involving the wave equation, 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pp.1236-1241, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01670643
Rock destruction effect on the stability of a drilling structure, Journal of Sound and Vibration, vol.233, issue.2, pp.235-254, 2000. ,
Fully coupled vibrations of actively controlled drillstrings, Journal of sound and vibration, vol.267, issue.5, pp.1029-1045, 2003. ,
Optimal control in networks of pipes and canals, SIAM Journal on Control and Optimization, vol.48, issue.3, pp.2032-2050, 2009. ,
Control and nonlinearity. Number 136 in Mathematical Surveys and Monographs, 2007. ,
A strict Lyapunov function for boundary control of hyperbolic systems of conservation laws, IEEE Trans. on Automatic Control, vol.52, issue.1, pp.2-11, 2007. ,
Methods of mathematical physics, 1989. ,
An introduction to infinite-dimensional linear systems theory, Texts in Applied Mathematics, vol.21, 1995. ,
Antiwindup design with guaranteed regions of stability: an LMI-based approach, IEEE Transactions on Automatic Control, vol.50, issue.1, pp.106-111, 2005. ,
Feedback stabilization of a hybrid PDE-ODE system: Application to an overhead crane, Mathematics of Control, Signals and Systems, vol.7, issue.1, pp.1-22, 1994. ,
Self-excited vibrations induced by drag bits, Journal of Energy Resources Technology, vol.112, issue.1, pp.54-61, 1990. ,
An extension of a theorem of A. M. Lyapunov to semi-groups of operators, Journal of Mathematical Analysis and Applications, vol.24, issue.2, pp.290-295, 1968. ,
Extending a theorem of A. M. Lyapunov to Hilbert space, Journal of Mathematical analysis and applications, vol.32, issue.3, pp.610-616, 1970. ,
An algorithm for computing Lyapunov functionals for some differentialdifference equations, Ordinary differential equations, pp.387-398, 1972. ,
Not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks, SIAM Journal on Control and Optimization, vol.26, issue.3, pp.697-713, 1988. ,
An example on the effect of time delays in boundary feedback stabilization of wave equations, SIAM Journal on Control and Optimization, vol.24, issue.1, pp.152-156, 1986. ,
Feedback systems: input-output properties, vol.55, 1975. ,
A distributed parameter systems view of control problems in drilling, 2nd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production OOGP, vol.48, pp.272-278, 2015. ,
Introduction to the theory and application of the Laplace transformation, 2012. ,
S-Variable Approach to LMI-Based Robust Control, Communications and Control Engineering, vol.17, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01760625
Event-based control of linear hyperbolic systems of conservation laws, Automatica, vol.70, pp.275-287, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01309671
Graduate studies in mathematics, Partial Differential Equations, 2010. ,
Boundary Observer Design for Coupled ODEsHyperbolic PDEs Systems, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02085133
Dynamics of a damped wave equation arising from MEMS, SIAM Journal on Applied Mathematics, vol.74, issue.4, pp.1025-1035, 2014. ,
Stability Results for the Wave Equation with Indefinite Damping, Journal of Differential Equations, vol.132, issue.2, pp.338-352, 1996. ,
Introduction to Time-Delay Systems, Analysis and Control. Birkhäuser, 2014. ,
Bounds on the response of a drilling pipe model, IMA Journal of Mathematical Control and Information, vol.27, issue.4, pp.513-526, 2010. ,
, Control Theory. Control Engineering, 2000.
A note on stability of time delay systems, IFAC Proceedings Volumes, vol.39, pp.555-560, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-00401031
Stability of time-delay systems with non-small delay, Proceedings of the 45th IEEE Conference on Decision and Control, pp.840-845, 2006. ,
The effect of boundary damping for the quasilinear wave equation, Journal of Differential Equations, vol.52, issue.1, pp.66-75, 1984. ,
Stability of time-delay systems, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00664367
Exponential stabilization of the wave equation by Dirichlet integral feedback, SIAM Journal on Control and Optimization, vol.53, issue.1, pp.526-546, 2015. ,
, Theory of functional differential equations. Number vol 3 in Applied Mathematical Sciences Series, 1977.
Introduction to functional differential equations. Applied mathematical sciences, 1977. ,
Effects of small delays on stability and control, Operator theory and analysis, pp.275-301, 2001. ,
Exact controllability and stabilization of a vibrating string with an interior point mass, SIAM journal on control and optimization, vol.33, issue.5, pp.1357-1391, 1995. ,
Rapid Exponential Stabilization of a 1-D Transmission Wave Equation with In-domain Anti-damping, Asian Journal of Control, vol.19, issue.6, pp.2017-2027, 2017. ,
Adaptive control of a flexible crane system with the boundary output constraint, IEEE Transactions on Industrial Electronics, vol.61, issue.8, pp.4126-4133, 2014. ,
Ill-posed distributed parameter systems: A control viewpoint, IEEE Trans. on Automatic Control, vol.36, issue.9, pp.1053-1057, 1991. ,
An integral high-order sliding mode control approach for stick-slip suppression in oil drillstrings, Petroleum Science and Technology, vol.27, issue.8, pp.788-800, 2009. ,
Simplified analytic stability test for systems with commensurate time delays, IEEE Proceedings D-Control Theory and Applications, vol.131, pp.52-56, 1984. ,
A Lyapunov functional for a matrix differencedifferential equation, Journal of Differential Equations, vol.29, issue.3, pp.439-451, 1978. ,
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. ,
Sur les fonctions convexes et les inégalités entre les valeurs moyennes. Acta mathematica, vol.30, pp.175-193, 1906. ,
Stability analysis of systems with delay-dependent coefficients, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01781318
On the relationship between zero criteria for two-variable polynomials and asymptotic stability of delay differential equations, IEEE Transactions on Automatic Control, vol.25, issue.5, pp.983-984, 1980. ,
Computer simulation of stick-slip friction in mechanical dynamic systems, Journal of dynamic systems, vol.107, issue.1, pp.100-103, 1985. ,
Nonlinear Systems. Pearson Education, 1996. ,
Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems, Automatica, vol.39, issue.1, pp.15-20, 2003. ,
Introduction to the theory and applications of functional differential equations, vol.463, 2013. ,
Stability of functional differential equations, vol.180, 1986. ,
Adaptive control of an anti-stable wave PDE, American Control Conference, 2009. ACC'09, pp.1505-1510, 2009. ,
Delay compensation for nonlinear, adaptive, and PDE systems, 2009. ,
Output-feedback stabilization of an unstable wave equation, Automatica, vol.44, issue.1, pp.63-74, 2008. ,
Nonlinear and adaptive control design, 1995. ,
Stabilization of nonlinear uncertain systems, 1998. ,
Boundary control of PDEs: A course on backstepping designs, vol.16, 2008. ,
Decay of solutions of wave equations in a bounded region with boundary dissipation, Journal of Differential equations, vol.50, issue.2, pp.163-182, 1983. ,
Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, Applied Mathematics and Optimization, vol.25, issue.2, pp.189-224, 1992. ,
Effect of drillstring vibrations on MWD pressure pulse signals, Journal of Energy Resources Technology, vol.112, issue.2, pp.84-89, 1990. ,
Transformation theory of non-linear differential equations of the second order, Annals of Mathematics, pp.723-737, 1944. ,
Time-varying sliding mode adaptive control for rotary drilling system, JCP, vol.6, issue.3, pp.564-570, 2011. ,
Coupled axialtorsional dynamics in rotary drilling with state-dependent delay: stability and control, Nonlinear Dynamics, vol.78, issue.3, pp.1891-1906, 2014. ,
YALMIP: A toolbox for modeling and optimization in MATLAB, IEEE International Symposium on Computer Aided Control Systems Design, pp.284-289, 2005. ,
Forced wave motion with internal and boundary damping, Journal of applied physics, vol.111, p.2012 ,
Stability and stabilization of infinite dimensional systems with applications, 2012. ,
The general problem of the stability of motion, International journal of control, vol.55, issue.3, pp.531-534, 1992. ,
Global stabilization of a kortewegde vries equation with saturating distributed control, SIAM Journal on Control and Optimization, vol.55, issue.3, pp.1452-1480, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01367622
System analysis via integral quadratic constraints, IEEE Transactions on Automatic Control, vol.42, issue.6, pp.819-830, 1997. ,
Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs, 2012. ,
Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness, vol.45, pp.1182-1194, 2009. ,
Nonlinear semigroups, vol.109, 1992. ,
A dynamic control law for the wave equation, Automatica, vol.30, issue.11, pp.1785-1792, 1994. ,
On the stabilization and stability robustness against small delays of some damped wave equations, IEEE Trans. on Automatic Control, vol.40, issue.9, pp.1626-1630, 1995. ,
An exponential stability result for the wave equation, Automatica, vol.38, issue.4, pp.731-735, 2002. ,
, Lineare differentialgleichungen mit nacheilendem argument, 1955.
An alternative characterization of bit-sticking phenomena in a multi-degree-of-freedom controlled drillstring, Nonlinear Analysis: Real World Applications, vol.10, pp.3162-3174, 2009. ,
Sliding-mode control of a multi-DOF oilwell drillstring with stick-slip oscillations, Proceedings of the American Control Conference, pp.3837-3842, 2007. ,
Practical approach to modeling and controlling stick-slip oscillations in oil-well drill-strings, Proceedings of the 2004 IEEE International Conference on Control Applications, vol.2, pp.1454-1460, 2004. ,
Delay effects on stability: a robust control approach, vol.269, 2001. ,
URL : https://hal.archives-ouvertes.fr/hal-02183198
An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems, IEEE Transactions on Automatic Control, vol.47, issue.5, pp.793-797, 2002. ,
A practical method for analyzing the stability of neutral type LTI-time delayed systems, Automatica, vol.40, issue.5, pp.847-853, 2004. ,
The complex structured singular value, Automatica, vol.29, issue.1, pp.71-109, 1993. ,
Semigroups of linear operators and applications to partial differential equations, vol.44, 1983. ,
Quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation, Automatica, vol.43, issue.5, pp.795-804, 2007. ,
A new state-space representation for coupled PDEs and scalable Lyapunov stability analysis in the SOS framework, 57th Annual Conference on Decision and Control (CDC), pp.545-550, 2018. ,
Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs, 2019. ,
Wave equation with conebounded control laws, IEEE Trans. on Automatic Control, vol.61, issue.11, pp.3452-3463, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01448483
Application of Liapunov's method to problems in the stability of systems with a delay, Automat. i Telemeh, vol.21, 1960. ,
A stability test for systems with delays, Proceedings of the joint automatic control conference, p.9, 1980. ,
A simplified model to explore the root cause of stick-slip vibrations in drilling systems with drag bits, Journal of Sound and Vibration, vol.305, issue.3, pp.432-456, 2007. ,
Boundary control of a wave equation with in-domain damping. Theses, 2018. ,
URL : https://hal.archives-ouvertes.fr/tel-01943937
Backstepping observer based-control for an anti-damped boundary wave PDE in presence of in-domain viscous damping, 55th IEEE Conference on Decision and Control (CDC), 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01413025
Lyapunov stability of coupled systems involving a transport equation. Theses, Institut supérieur de l'aéronautique et de l'espace, 2018. ,
URL : https://hal.archives-ouvertes.fr/tel-01975119
Stabilité de Lyapunov de systèmes couplés impliquant uneéquation de transport, 2018. ,
Tractable sufficient stability conditions for a system coupling linear transport and differential equations, Systems & Control Letters, vol.110, pp.1-8, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01354073
Lyapunov stability analysis of a system coupled to a hyperbolic PDE with potential, European Control Conference (ECC 2018), 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01799391
Backstepping and flatness approaches for stabilization of the stick-slip phenomenon for drilling, IFAC Proceedings Volumes, vol.46, pp.779-784, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00873605
Analysis and Control of Oilwell Drilling Vibrations: A Time-Delay Systems Approach, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01123773
The control of drilling vibrations: A coupled PDE-ODE modeling approach, International Journal of Applied Mathematics and Computer Science, 2016. ,
A control oriented guided tour in oilwell drilling vibration modeling, Annual Reviews in Control, vol.42, pp.100-113, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01425845
Semidynamical Systems in Infinite Dimensional Spaces. Applied mathematical sciences, 1981. ,
LPV control and full block multipliers, Automatica, vol.37, issue.3, pp.361-375, 2001. ,
Stability analysis by dynamic dissipation inequalities: On merging frequency-domain techniques with time-domain conditions. Systems and Control Letters, 2018. ,
Construction of observers for hyperbolic systems, 2018. ,
H ? control for suppressing stick-slip in oil well drillstrings, IEEE Control Systems, vol.18, pp.19-30, 1998. ,
Jensen's and Wirtinger's inequalities for time-delay systems, IFAC Proceedings Volumes, vol.46, pp.343-348, 2013. ,
Wirtinger-based integral inequality: application to time-delay systems, Automatica, vol.49, issue.9, pp.2860-2866, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00855159
Hierarchy of LMI conditions for the stability analysis of time-delay systems, Systems & Control Letters, vol.81, pp.1-7, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01065142
Hierarchical estimation of the region of attraction for systems subject to a state delay and a saturated input, 2017 IEEE European Control Conference (CDC), 2019. ,
Stability and stabilization of systems with time delay, IEEE Control Systems, vol.31, issue.1, pp.38-65, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00664367
Degenerate cases in using the direct method, ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp.2201-2210, 2003. ,
A controller to overcome dead time, ISA J, vol.6, pp.28-33, 1959. ,
Closed-form boundary state feedbacks for a class of 1-D partial integro-differential equations, IEEE Transactions on Automatic Control, vol.49, issue.12, pp.2185-2202, 2004. ,
Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary, Systems & Control Letters, vol.58, issue.8, pp.617-623, 2009. ,
The ISS philosophy as a unifying framework for stability-like behavior, vol.2, pp.443-467, 2000. ,
Input to state stability: Basic concepts and results, Nonlinear and optimal control theory, pp.163-220, 2008. ,
State and output feedback boundary control for a coupled PDE-ODE system, Systems & Control Letters, vol.60, issue.8, pp.540-545, 2011. ,
Stability analysis of coupled linear ODE-hyperbolic PDE systems with two time scales, Automatica, vol.85, pp.386-396, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01388874
Stability analysis of a singularly perturbed coupled ODE-PDE system, 54th IEEE Conference on Decision and Control (CDC), pp.4591-4596, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01276239
Stability and stabilization of linear systems with saturating actuators, 2011. ,
Régulation des systèmesà paramètres distribués : application au forage, 2018. ,
Dos Santos Martins. Regulation of inhomogeneous drilling model with a P-I controller, IEEE Transactions on Automatic Control, 2019. ,
Regulation of the downside angular velocity of a drilling string with a P-I controller, pp.2647-2652, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-02014813
SDPT3 -a MATLAB software package for semidefinite programming, version 1.3. Optimization methods and software, vol.11, pp.545-581, 1999. ,
On the effective control of torsional vibrations in drilling systems, Journal of Sound and Vibration, vol.224, issue.1, pp.101-122, 1999. ,
Wellposedness, controllability and stabilizability of systems governed by partial differential equations, 2004. ,
Observation and control for operator semigroups, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00590673
Robust stability and performance analysis based on integral quadratic constraints, European Journal of Control, vol.31, pp.1-32, 2016. ,
Quasipolynomial mapping based rootfinder for analysis of time delay systems, IFAC Proceedings Volumes, vol.36, pp.227-232, 2003. ,
Vibration problems in engineering, 1990. ,
Static output feedback control via PDE boundary and ODE measurements in linear cascaded ODE-beam systems, Automatica, vol.50, issue.11, pp.2787-2798, 2014. ,
On the input-output stability of time-varying nonlinear feedback systems part one: Conditions derived using concepts of loop gain, conicity, and positivity, IEEE Transactions on Automatic Control, vol.11, issue.2, pp.228-238, 1966. ,
Sliding mode control of rotary drilling system with stick slip oscillation, 2nd International Workshop on Intelligent Systems and Applications, pp.1-4, 2010. ,
Handbook of differential equations, vol.1, 1998. ,