, , p.152
155 8.3.1 Backstepping transformation of the original system (8.36)-(8.39). .. .. . 155 8.3.2 Backstepping transformation of the error system ,
Backstepping transformation of the original system (8.36)-(8.39) and pseudosteady state, Output regulation: Input-to-State Stability and proof of Theorem 8.1.3 168 8.4.1 ,
Backstepping transformation of the error system ,
Simulation results and concluding remarks ,
Disturbance rejection in the interior domain of linear 2×2 hyperbolic systems, IEEE Transactions on Automatic Control, vol.60, issue.1, pp.186-191, 2015. ,
Limits of controller performance in the heave disturbance attenuation problem, European Control Conference (ECC), pp.1071-1076, 2013. ,
Disturbance rejection in 2x2 linear hyperbolic systems, IEEE Transactions on Automatic Control, vol.58, issue.5, pp.1095-1106, 2013. ,
Leak detection, size estimation and localization in pipe flows, IEEE Transactions on Automatic Control, vol.61, issue.1, pp.246-251, 2016. ,
Delay-robust control design for heterodirectional linear coupled hyperbolic pdes, IEEE Transactions on Automatic Control, 2018. ,
DOI : 10.1109/tac.2018.2798818
URL : https://hal.archives-ouvertes.fr/hal-01585911
Backstepping pde design: A convex optimization approach, IEEE Transactions on Automatic Control, 2017. ,
DOI : 10.1109/tac.2017.2757088
Modeling of Two-Phase Flow for Estimation and Control of Drilling Operations, 2016. ,
Delay-robust stabilization of a hyperbolic pde-ode system. Automatica, provisionally accepted, 2018. ,
An adaptive observer design for n + 1 coupled linear hyperbolic pdes based on swapping, IEEE Transactions on Automatic Control, vol.61, issue.12, pp.3979-3990, 2016. ,
DOI : 10.1109/tac.2016.2530624
Boundary parameter and state estimation in general linear hyperbolic pdes, IFAC-PapersOnLine, vol.49, issue.8, pp.104-110, 2016. ,
DOI : 10.1016/j.ifacol.2016.07.426
Minimum time control of heterodirectional linear coupled hyperbolic PDEs, Automatica, vol.71, pp.300-307, 2016. ,
DOI : 10.1016/j.automatica.2016.05.030
URL : https://hal.archives-ouvertes.fr/hal-01477700
Two-sided boundary stabilization of two linear hyperbolic pdes in minimum time, Decision and Control (CDC), 2016 IEEE 55th Conference on, pp.3118-3124, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01286860
Two sided boundary stabilization of heterodirectional linear coupled hyperbolic pdes, IEEE Transactions on Automatic Control, 2017. ,
DOI : 10.1109/tac.2017.2763320
URL : https://hal.archives-ouvertes.fr/hal-01318708
Control-oriented drift-flux modeling of single and two-phase flow for drilling, Proceedings of the ASME 2014 Dynamic Systems and Control Conference, 2014. ,
DOI : 10.1115/dscc2014-6121
URL : https://hal.archives-ouvertes.fr/hal-01499936
A methodology for classifying operating regimes in underbalanced-drilling operations, SPE Journal, vol.21, issue.02, pp.423-433, 2016. ,
DOI : 10.2118/178920-pa
An explicit mapping from linear first order hyperbolic pdes to difference systems, Systems & Control Letter, 2018. ,
DOI : 10.1016/j.sysconle.2018.11.012
URL : https://hal.archives-ouvertes.fr/hal-02014310
Modeling and avoidance of heave-induced resonances in offshore drilling, SPE Drilling & Completion, vol.29, issue.04, pp.454-464, 2014. ,
On stability of switched linear hyperbolic conservation laws with reflecting boundaries, Hybrid Systems: Computation and Control, pp.602-605, 2008. ,
Feedback systems: an introduction for scientists and engineers, 2010. ,
Late-lumping backstepping control of partial differential equations. Automatica, under review, 2018. ,
DOI : 10.1016/j.automatica.2018.11.024
URL : https://hal.archives-ouvertes.fr/hal-01740646
Backstepping-forwarding control and observation for hyperbolic pdes with fredholm integrals, IEEE Transactions on, vol.60, issue.8, pp.2145-2160, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01225219
Differential-difference equations, 1963. ,
On boundary feedback stabilization of non-uniform linear 2× 2 hyperbolic systems over a bounded interval, Systems & Control Letters, vol.60, issue.11, pp.900-906, 2011. ,
Stability and boundary stabilization of 1-d hyperbolic systems, 2016. ,
DOI : 10.1007/978-3-319-32062-5
URL : https://hal.archives-ouvertes.fr/hal-01449504
Unbounded control operators: Hyperbolic equations with control on the boundary. Representation and Control of Infinite Dimensional Systems, pp.459-475, 2007. ,
DOI : 10.1007/978-1-4612-2750-2_5
Approximation in LQR problems for infinite dimensional systems with unbounded input operators, Journal of Mathematical Systems Estimation and Control, vol.7, pp.119-119, 1997. ,
On non-convergence of adjoint semigroups for control systems with delays, SIAM Jour. Control and Optim, vol.26, issue.6, pp.1442-1454, 1988. ,
The linear regulator problem for parabolic systems, SIAM Journal on Control and Optimization, vol.22, issue.5, pp.684-698, 1984. ,
Adaptive output-feedback stabilization of non-local hyperbolic pdes, Automatica, vol.50, issue.10, pp.2692-2699, 2014. ,
Nonlinear control under nonconstant delays, 2013. ,
Compensation of wave actuator dynamics for nonlinear systems, IEEE Transactions on Automatic Control, vol.59, issue.6, pp.1555-1570, 2014. ,
Growth bound of delay-differential algebraic equations, Comptes Rendus Mathematique, vol.351, issue.15, pp.645-648, 2013. ,
Analyse complexe et applications. Mines ParisTech, 2018. ,
, Commande robuste de systèmes à retard variable: Contributions théoriques et applications au contrôle moteur, 2012.
Adaptive control scheme for uncertain time-delay systems, Automatica, vol.48, issue.8, pp.1536-1552, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00733308
Prediction-based stabilization of linear systems subject to input-dependent input delay of integral-type, IEEE Transactions on Automatic Control, vol.59, issue.9, pp.2385-2399, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01059870
Prediction-based control of linear input-delay system subject to state-dependent state delay-application to suppression of mechanical vibrations in drilling, IFAC-PapersOnLine, vol.49, issue.8, pp.111-117, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01348998
Delay-adaptive predictor feedback for systems with unknown long actuator delay, IEEE Transactions on Automatic Control, vol.55, issue.9, pp.2106-2112, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00951855
Adaptive output feedback for oil drilling stickslip instability modeled by wave pde with anti-damped dynamic boundary, American Control Conference (ACC), pp.386-391, 2014. ,
Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem, vol.20, 2000. ,
Functional analysis, Sobolev spaces and partial differential equations, 2010. ,
Stability analysis of linear 2×2 hyperbolic pdes. submitted to, International Journal of Robust and Nonlinear Control, 2018. ,
Mesh independence of KleinmanNewton iterations for Riccati equations in Hilbert space, SIAM Jour. Control and Optim, vol.47, issue.5, pp.2663-2692, 2008. ,
Input-output stability of linear time-invariant systems, IEEE Transactions on Automatic Control, vol.15, issue.3, pp.316-319, 1970. ,
A lyapunov approach to control irrigation canals modeled by saint-venant equations, Proc. European Control Conference, 1999. ,
On quadratic liapunov functionals for linear difference equations, Linear Algebra and its applications, vol.240, pp.41-64, 1996. ,
DOI : 10.1016/0024-3795(94)00183-9
URL : https://doi.org/10.1016/0024-3795(94)00183-9
Andréa Novel. Dissipative boundary conditions for one-dimensional nonlinear hyperbolic systems, SIAM Journal on Control and Optimization, vol.47, issue.3, pp.1460-1498, 2008. ,
Stabilization and controllability of firstorder integro-differential hyperbolic equations, Journal of Functional Analysis, vol.271, issue.12, pp.3554-3587, 2016. ,
DOI : 10.1016/j.jfa.2016.08.018
URL : https://hal.archives-ouvertes.fr/hal-01224012
Finite-time boundary stabilization of general linear hyperbolic balance laws via fredholm backstepping transformation, Automatica, vol.84, pp.95-100, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01437107
Boundary controllability of nonlinear hyperbolic systems, SIAM Journal on Control, vol.7, issue.2, pp.198-212, 1969. ,
Well-posedness of boundary control systems, SIAM Jour. Control & Optim, vol.42, issue.4, pp.1244-1265, 2003. ,
, Control and nonlinearity. Number 136, 2009.
Infinite dimensional linear systems theory, Lecture Notes in Control and Information Sciences, vol.8, 1978. ,
Finite-dimensional compensators for infinitedimensional systems with unbounded input operators, SIAM journal on control and optimization, vol.24, issue.4, pp.797-816, 1986. ,
DOI : 10.1137/0324050
URL : http://www.math.ethz.ch/~salamon/PREPRINTS/curtain-salamon86.pdf
Feedback stabilization for a scalar conservation law with PID boundary control, Chinese Annals of Mathematics, Series B, vol.36, issue.5, pp.763-776, 2015. ,
DOI : 10.1007/s11401-015-0975-8
Local exponential h 2 stabilization of a 2× 2 quasilinear hyperbolic system using backstepping, SIAM Journal on Control and Optimization, vol.51, issue.3, pp.2005-2035, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00726867
An introduction to infinite-dimensional linear systems theory, vol.21, 2012. ,
Suite des recherches sur la courbe que forme une corde tendue, mise en vibration, Histoire de l'Académie Royale des Sciences et des Belles Lettres de Berlin, pp.220-249, 1749. ,
Stability and asymptotic observers of binary distillation processes described by nonlinear convection/diffusion models, American Control Conference (ACC), pp.3352-3358, 2012. ,
DOI : 10.1109/acc.2012.6315036
URL : https://hal.archives-ouvertes.fr/hal-00738684
Lyapunov exponential stability of 1-d linear hyperbolic systems of balance laws, Automatica, vol.48, issue.1, pp.109-114, 2012. ,
Boundary actuation structure of linearized two-phase flow, American Control Conference (ACC), pp.3759-3764, 2010. ,
DOI : 10.1109/acc.2010.5531552
Stability of linear continuous-time difference equations with distributed delay: Constructive exponential estimates, International Journal of Robust and Nonlinear Control, vol.25, issue.17, pp.3195-3209, 2015. ,
DOI : 10.1002/rnc.3249
URL : https://hal.archives-ouvertes.fr/hal-01256045
Exponential stability with decay rate estimation for linear difference equations, IEEE Transactions on Automatic Control, vol.61, issue.1, pp.252-257, 2016. ,
DOI : 10.1109/tac.2015.2437519
URL : https://hal.archives-ouvertes.fr/hal-01256040
Backstepping design of robust state feedback regulators for linear 2 × 2 hyperbolic systems, IEEE Transactions on Automatic Control, 2016. ,
Finite-time output regulation for linear 2 × 2 hyperbolic systems using backstepping, Automatica, vol.75, pp.54-62, 2017. ,
DOI : 10.1016/j.automatica.2016.09.020
Boundary feedback control in networks of open channels, Automatica, vol.39, issue.8, pp.1365-1376, 2003. ,
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 boundary control problems for linear semigroups, Israel Journal of Mathematics, vol.51, issue.3, pp.177-207, 1985. ,
Dynamics and control of slugging in oil production, Centre Automatique et Systèmes (CAS), 2011. ,
URL : https://hal.archives-ouvertes.fr/pastel-00617949
A distributed parameter systems view of control problems in drilling, to appear in 2nd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production, 2015. ,
Stabilization of coupled linear heterodirectional hyperbolic pde-ode systems, Automatica, vol.87, pp.281-289, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01376564
An adaptive observer for hyperbolic systems with application to underbalanced drilling, IFAC Proceedings Volumes, vol.47, pp.11391-11397, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01059860
A backstepping boundary observer for a class of linear first-order hyperbolic systems, Control Conference (ECC), 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01499940
, , pp.1597-1602, 2013.
Modeling and control of complex physical systems: the port-Hamiltonian approach, 2009. ,
Stabilization of a system of n + 1 coupled first-order hyperbolic linear pdes with a single boundary input, IEEE Transactions on Automatic Control, vol.58, issue.12, pp.3097-3111, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-01499945
Backstepping stabilization of an underactuated 3× 3 linear hyperbolic system of fluid flow equations, American Control Conference (ACC), pp.3365-3370, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00637713
Andréa Novel. Boundary control with integral action for hyperbolic systems of conservation laws: Stability and experiments, Automatica, vol.44, issue.5, pp.1310-1318, 2008. ,
Modeling and simulation for automatic control, Marine Cybernetics Trondheim, vol.76, 2002. ,
Volterra?s integral equation of the second kind, with discontinuous kernel. ii, Transactions of the American Mathematical Society, vol.12, issue.4, pp.429-472, 1911. ,
Controllability of evolution equations. Number 34, 1996. ,
Stability of linear descriptor systems with delay: a lyapunov-based approach, Journal of Mathematical Analysis and Applications, vol.273, issue.1, pp.24-44, 2002. ,
H ?-control of linear state-delay descriptor systems: an LMI approach, Linear Algebra and its Applications, vol.351, pp.271-302, 2002. ,
Time-delayed boundary feedback stabilization of the isothermal euler equations with friction, Math. Control Relat. Fields, vol.1, issue.4, pp.469-491, 2011. ,
A novel approach to exact slow-fast decomposition of linear singularly perturbed systems with small delays, SIAM Journal on Control and Optimization, vol.55, issue.1, pp.236-274, 2017. ,
Stability of time-delay systems, Birkhäuser, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00664367
The effect of boundary damping for the quasilinear wave equation, Journal of Differential Equations, vol.52, issue.1, pp.66-75, 1984. ,
Boundary exponential stabilization of 1-d inhomogeneous quasilinear hyperbolic systems, 2015. ,
Control of homodirectional and general heterodirectional linear coupled hyperbolic PDEs, IEEE Transactions on Automatic Control, vol.61, issue.11, pp.3301-3314, 2016. ,
DOI : 10.1109/tac.2015.2512847
URL : https://hal.archives-ouvertes.fr/hal-01429825
Strong stabilization of neutral functional differential equations, IMA Journal of Mathematical Control and Information, vol.19, pp.5-23, 2002. ,
DOI : 10.1093/imamci/19.1_and_2.5
Admissible input elements for systems in Hilbert space and a carleson measure criterion, SIAM Journal on Control and Optimization, vol.21, issue.4, pp.614-640, 1983. ,
DOI : 10.1137/0321037
Introduction to functional differential equations, 1993. ,
DOI : 10.1007/978-1-4612-4342-7
The Trotter-Kato theorem and approximation of PDEs. Mathematics of Computation of the, vol.67, pp.21-44, 1998. ,
DOI : 10.1090/s0025-5718-98-00915-6
URL : https://www.ams.org/mcom/1998-67-221/S0025-5718-98-00915-6/S0025-5718-98-00915-6.pdf
The theory of approximation, vol.11, 1930. ,
An efficient implementation of backstepping observers for time-varying parabolic pdes, IFAC Proceedings Volumes, vol.45, pp.798-803, 2012. ,
DOI : 10.3182/20120215-3-at-3016.00141
Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Communications on pure and applied mathematics, vol.13, issue.4, pp.551-585, 1960. ,
Linear systems, vol.156, 1980. ,
Output-feedback stabilization of an unstable wave equation, Automatica, vol.44, issue.1, pp.63-74, 2008. ,
DOI : 10.1016/j.automatica.2007.05.012
On the relation of delay equations to first-order hyperbolic partial differential equations. ESAIM: Control, Optimisation and Calculus of Variations, vol.20, pp.894-923, 2014. ,
Nonlinear stabilization of shock-like unstable equilibria in the viscous burgers pde, IEEE Transactions on Automatic Control, vol.53, issue.7, pp.1678-1683, 2008. ,
Nonlinear control of the viscous burgers equation: Trajectory generation, tracking, and observer design, Journal of Dynamic Systems, Measurement, and Control, vol.131, issue.2, p.21012, 2009. ,
DOI : 10.1115/1.3023128
A new stick-slip prevention system, SPE/IADC Drilling Conference and Exhibition, 2009. ,
DOI : 10.2118/119660-ms
Lyapunov tools for predictor feedbacks for delay systems: Inverse optimality and robustness to delay mismatch, Automatica, vol.44, issue.11, pp.2930-2935, 2008. ,
DOI : 10.1109/acc.2008.4587273
Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays, Systems & Control Letters, vol.57, issue.9, pp.750-758, 2008. ,
DOI : 10.1016/j.sysconle.2008.02.005
Boundary control of PDEs: A course on backstepping designs, vol.16, 2008. ,
Robust output regulation of 2 x 2 hyperbolic systems: Control law and input-to-state stability, American and Control Conference, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01499686
Approximations of riccati equation for abstract boundary control problems applications to hyperbolic systems. Numerical functional analysis and optimization, vol.8, pp.207-243, 1986. ,
Control of 2 × 2 linear hyperbolic systems: Backstepping-based trajectory generation and PI-based tracking, Systems & Control Letters, vol.86, pp.24-33, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01188195
Adding an integrator to backstepping: Output disturbances rejection for linear hyperbolic systems, American Control Conference (ACC), pp.3422-3428, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01358718
Gap and density theorems, vol.26, 1940. ,
DOI : 10.1090/coll/026
Boundary control of hyperbolic conservation laws using a frequency domain approach, Automatica, vol.45, issue.3, pp.647-656, 2009. ,
A semigroup approach to port hamiltonian systems associated with linear skew symmetric operator, 16th International Symposium on Mathematical Theory of Networks and Systems, 2004. ,
Dirac structures and boundary control systems associated with skew-symmetric differential operators, SIAM journal on control and optimization, vol.44, issue.5, pp.1864-1892, 2005. ,
Global classical solutions for quasilinear hyperbolic systems, vol.32, 1994. ,
Exact boundary observability for quasilinear hyperbolic systems, vol.14, pp.759-766, 2008. ,
Controllability and observability for quasilinear hyperbolic systems, American Institute of Mathematical Sciences Springfield, 2010. ,
Optimal control of systems governed by partial differential equations problèmes aux limites, 1971. ,
Contrôlabilité exacte, stabilisation et perturbations de systemes distribués. tome 1. contrôlabilité exacte, Rech. Math. Appl, vol.8, 1988. ,
Exact controllability, stabilization and perturbations for distributed systems, SIAM review, vol.30, issue.1, pp.1-68, 1988. ,
Semi-global c1 solution to the mixed initial-boundary value problem for quasilinear hyperbolic systems, Chinese Annals of Mathematics, vol.22, issue.03, pp.325-336, 2001. ,
Dissipative operators in a banach space, Pacific Journal of Mathematics, vol.11, issue.2, pp.679-698, 1961. ,
Local exact boundary controllability for a class of quasilinear hyperbolic systems, Chinese Annals of Mathematics, vol.23, issue.02, pp.209-218, 2002. ,
URL : https://hal.archives-ouvertes.fr/hal-00086440
Exact boundary controllability for quasi-linear hyperbolic systems, SIAM Journal on Control and Optimization, vol.41, issue.6, pp.1748-1755, 2003. ,
Strong (weak) exact controllability and strong (weak) exact observability for quasilinear hyperbolic systems, Chinese Annals of Mathematics, Series B, vol.31, issue.5, pp.723-742, 2010. ,
Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop, SIAM Journal on Control and Optimization, vol.34, issue.2, pp.572-600, 1996. ,
Feedback semigroups and cosine operators for boundary feedback parabolic and hyperbolic equations, Journal of Differential Equations, vol.47, issue.2, pp.246-272, 1983. ,
DOI : 10.1016/0022-0396(83)90036-0
URL : https://doi.org/10.1016/0022-0396(83)90036-0
,
, Applied mathematics & optimization, vol.10, pp.275-286, 1983.
Differential and algebraic riccati equations with application to boundary/point control problems: continuous theory and approximation theory, Lecture notes in control and Information Sciences, vol.164, pp.1-160, 1991. ,
, Control Theory for Partial Differential Equations: Continuous and Approximation Theories, volume I, 2000.
DOI : 10.1017/cbo9781107340848
, Control Theory for Partial Differential Equations: Continuous and Approximation Theories, volume II, 2000.
DOI : 10.1017/cbo9781107340848
Contrôlabilité exacte frontière pour les équations des ondes quasi linéaires unidimensionnelles, Comptes Rendus Mathematique, vol.337, issue.4, pp.271-276, 2003. ,
DOI : 10.1016/s1631-073x(03)00327-3
Exponential stability of linear continuous time difference systems with multiple delays, Systems & Control Letters, vol.62, issue.10, pp.811-818, 2013. ,
On the synthesis of boundary control laws for distributed port-hamiltonian systems, IEEE transactions on automatic control, vol.62, issue.4, pp.1700-1713, 2017. ,
Finite spectrum assignment of unstable time-delay systems with a safe implementation, IEEE Transactions on Automatic Control, vol.48, issue.12, pp.2207-2212, 2003. ,
Ordinary differential equations, 2007. ,
Stability and stabilization of time-delay systems: an eigenvalue-based approach. SIAM, 2007. ,
Convergence of controllers designed using state-space methods, IEEE Trans. Auto. Cont, vol.39, issue.10, pp.2100-2104, 1994. ,
Design of finite-dimensional controllers for infinite-dimensional systems by approximation, Jour. of Mathematical Systems, Estimation and Control, vol.4, issue.2, pp.1-30, 1994. ,
H ? output feedback control of infinite-dimensional systems via approximation, Systems and Control Letters, vol.44, issue.3, pp.211-217, 2001. ,
Control of systems governed by partial differential equations. The Control Theory Handbook, 2010. ,
Every stabilizing dead-time controller has an observerpredictor-based structure, Automatica, vol.39, pp.1747-1754, 2003. ,
DOI : 10.1016/s0005-1098(03)00182-1
URL : http://leo.technion.ac.il/publications/YoulaDelay/YoulaDelay.pdf
Strong stability of neutral equations with an arbitrary delay dependency structure, SIAM Journal on Control and Optimization, vol.48, issue.2, pp.763-786, 2009. ,
Transmission lines and wave propagation, 2000. ,
Flatness-based feedback control of diffusion-convectionreaction systems via k-summable power series, IFAC Proceedings Volumes, vol.37, pp.177-182, 2004. ,
Delay effects on stability: a robust control approach, vol.269, 2001. ,
On delay-dependent stability under model transformations of some neutral linear systems, International Journal of Control, vol.74, issue.6, pp.609-617, 2001. ,
Semigroups of linear operators and applications to partial differential equations, vol.44, 2012. ,
On the asymptotic stability of coupled delay differential and continuous time difference equations, Automatica, vol.41, issue.1, pp.107-112, 2005. ,
Lyapunov functions for switched linear hyperbolic systems, IFAC Proceedings Volumes, vol.45, pp.382-387, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00734469
Introduction to Fourier analysis and wavelets, vol.102, 2002. ,
DOI : 10.1090/gsm/102
Converse lyapunov-krasovskii theorems for systems described by neutral functional differential equations in hale's form, International Journal of Control, vol.86, issue.2, pp.232-243, 2013. ,
Unbounded control and observation systems and their duality, SIAM Journal on Control and Optimization, vol.16, issue.4, pp.535-545, 1978. ,
DOI : 10.1137/0316036
Global smooth solutions of dissipative boundary-value problems for 1st order quasilinear hyperbolic systems, Chinese annals of mathematics series B, vol.6, issue.3, pp.289-298, 1985. ,
Simplified fluid transmission line model for pneumatic control applications, Proc. 14th Scandinavian International Conference on Fluid Power (SICFP15), 2015. ,
An introduction to partial differential equations, vol.13, 2006. ,
Nonharmonic fourier series in the control theory of distributed parameter systems, Journal of Mathematical Analysis and Applications, vol.18, issue.3, pp.542-560, 1967. ,
On boundary-value controllability of linear symmetric hyperbolic systems, Mathematical Theory of Control, pp.312-321, 1967. ,
Control theory of hyperbolic equations related to certain questions in harmonic analysis and spectral theory, Journal of Mathematical Analysis and Applications, vol.40, issue.2, pp.336-368, 1972. ,
Canonical forms and spectral determination for a class of hyperbolic distributed parameter control systems, Journal of Mathematical Analysis and Applications, vol.62, issue.1, pp.186-225, 1978. ,
Controllability and stabilizability theory for linear partial differential equations: recent progress and open questions, Siam Review, vol.20, issue.4, pp.639-739, 1978. ,
DOI : 10.1137/1020095
Neutral pde canonical representations of hyperbolic systems, The Journal of Integral Equations and Applications, pp.129-166, 1991. ,
DOI : 10.1216/jiea/1181075603
URL : https://doi.org/10.1216/jiea/1181075603
Infinite-dimensional linear systems with unbounded control and observation: a functional analytic approach, Transactions of the American Mathematical Society, vol.300, issue.2, pp.383-431, 1987. ,
Boundary stabilization of a 1-d wave equation with in-domain antidamping, SIAM Journal on Control and Optimization, vol.48, issue.6, pp.4014-4031, 2010. ,
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
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. ,
Backstepping observers for a class of parabolic PDEs, Systems & Control Letters, vol.54, issue.7, pp.613-625, 2005. ,
Boundary control of an anti-stable wave equation with anti-damping on the uncontrolled boundary, Systems & Control Letter, vol.58, issue.8, pp.617-623, 2009. ,
Boundary feedback stabilization for a quasi-linear wave equation, Control Theory for Distributed Parameter Systems and Applications, pp.221-237, 1983. ,
A controller to overcome dead time, ISA J, vol.6, pp.28-33, 1959. ,
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
Global smooth solutions of dissipative boundary value problems for first order quasilinear hyperbolic systems. Chinese annals of mathematic, series B, vol.6, pp.289-298, 1985. ,
Sliding mode control to the stabilization of a linear 2 × 2 hyperbolic system with boundary input disturbance, American Control Conference, pp.1027-1032, 2014. ,
Local exponential h-2 stabilization of a 2× 2 quasilinear hyperbolic system using backstepping, Decision and Control and European Control Conference, pp.1329-1334, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00726867
Input-output stability of a broad class of linear time-invariant multivariable systems, SIAM J. Control, vol.10, issue.1, pp.203-209, 1972. ,
Marcum q-functions and explicit kernels for stabilization of 2× 2 linear hyperbolic systems with constant coefficients, Systems & Control Letters, vol.68, pp.33-42, 2014. ,
Bilateral boundary control of one-dimensional firstand second-order PDEs using infinite-dimensional backstepping, Decision and Control (CDC), 2016 IEEE 55th Conference on, pp.537-542, 2016. ,
Taking a step back: A brief history of PDE backstepping, IFAC Proceedings Volumes, 2017. ,
Backstepping boundary stabilization and state estimation of a 2× 2 linear hyperbolic system, Decision and Control and European Control Conference, pp.4937-4942, 2011. ,
A bound on the boundary input map for parabolic equations with application to time optimal control, SIAM Journal on Control and Optimization, vol.17, issue.5, pp.652-671, 1979. ,
Admissibility of unbounded control operators, SIAM Journal on Control and Optimization, vol.27, issue.3, pp.527-545, 1989. ,
Linear and nonlinear waves, vol.42, 2011. ,
On approximation and implementation of transformation based feedback laws for distributed parameter systems, IFAC Proceedings Volumes, 2017. ,
Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, vol.7, pp.421-442, 2002. ,
Delayed feedback control of uncertain systems with timevarying input delay, Automatica, vol.41, issue.2, pp.233-240, 2005. ,
, Lectures on differential and integral equations, vol.10, 1960.
The boundary value problem for systems of first-order quasilinear hyperbolic equations, Chinese Annals of Mathematics Serie A, vol.7, pp.629-643, 1986. ,
Robust control of time-delay systems, 2006. ,