Backstepping in infinite dimension for a class of 7 parabolic distributed parameter systems, Math. Control Signals Systems, vol.16, issue.1, pp.44-75, 2003. ,
, Stability and boundary stabilization of 1-D hyperbolic systems
URL : https://hal.archives-ouvertes.fr/hal-01449504
, ume 88 of Progress in Nonlinear Differential Equations and their Applications, 2016.
Infinite Dimensional Backstepping-Style Feedback Transformations for a 12 ,
, Heat Equation with an Arbitrary Level of Instability, European Journal of Control, vol.8, issue.2, pp.165-175, 2002.
Functional analysis, Sobolev spaces and partial differential equations, p.14 ,
An introduction to frames and Riesz bases. Applied and Numerical Harmonic Analysis ,
, , 2016.
Coron and Brigitte d'Andréa Novel. Stabilization of a rotating body beam without damping ,
, IEEE Trans. Automat. Control, vol.43, issue.5, pp.608-618, 1998.
,
, Schrödinger equation. J. Math. Pures Appl, vol.115, issue.9, pp.24-73, 2018.
Stabilization and controllability of first-order integro-22 differential hyperbolic equations, J. Funct. Anal, vol.271, issue.12, pp.3554-3587, 2016. ,
Finite-time boundary stabilization of general linear hy-24 perbolic balance laws via Fredholm backstepping transformation, Automatica J. IFAC, vol.84, p.25, 2017. ,
Local rapid stabilization for a Korteweg-de Vries equation with a Neumann 26 boundary control on the right, J. Math. Pures Appl, vol.102, issue.9, pp.1080-1120, 2014. ,
Fredholm transform and local rapid stabilization for a Kuramoto-Sivashinsky 28 equation, J. Differential Equations, vol.259, issue.8, pp.3683-3729, 2015. ,
Null controllability and finite time stabilization for the heat 30 equations with variable coefficients in space in one dimension via backstepping approach, Arch. Ration. Mech. 31 Anal, vol.225, issue.3, pp.993-1023, 2017. ,
Control and nonlinearity, Mathematical Surveys and Monographs, vol.136, 2007. ,
Stabilization of control systems and nonlinearities, Proceedings of the 8th International, vol.35 ,
, Congress on Industrial and Applied Mathematics, p.36, 2015.
Local exponential H 2 stabilization 37 of a 2 × 2 quasilinear hyperbolic system using backstepping, SIAM J. Control Optim, vol.51, issue.3, p.38, 2013. ,
Motion planning and nonlinear simulations for a tank 39 containing a fluid, European Control Conference (ECC), pp.3232-3237, 1999. ,
Exponential stability of general 1-D quasilinear systems with source terms for the C 1 norm 41 under boundary conditions. preprint, 2017. ,
On boundary stability of inhomogeneous 2 × 2 1-D hyperbolic systems for the C 1 norm. 43 preprint, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01790104
Séries de Fourier et ondelettes. Cassini, p.45, 1998. ,
Output-feedback stabilization of an 1 unstable wave equation, IEEE Transactions on Automatic Control, vol.44, issue.1, pp.63-74, 2008. ,
Rapid boundary stabilization of linear distributed systems, SIAM J. Control Optim, vol.3, issue.5, pp.1591-1613, 1997. ,
Boundary control of PDEs, Advances in Design 5 and Control. Society for Industrial and Applied Mathematics (SIAM), vol.16, 2008. ,
Nonlinear and Adaptive Control Design ,
Backstepping boundary control of Burgers' equation with actuator dynamics ,
, Systems Control Lett, vol.41, issue.4, pp.291-303, 2000.
Boundary feedback stabilization of homogeneous equilibria in unstable fluid 12 mixtures, Internat. J. Control, vol.80, issue.6, pp.982-989, 2007. ,
Discontinuous feedback stabilization of minimum-phase semilinear infinite-14 dimensional systems with application to chemical tubular reactor, IEEE Trans. Automat. Control, vol.47, issue.8, pp.1293-1308, 2002. ,
, Stabilizability and optimal control. Funkcial. Ekvac, vol.11, p.17, 1968.
Semigroups of linear operators and applications to partial differential equations, vol.44, p.18 ,
, Applied Mathematical Sciences, 1983.
Distributed nonlinear 20 control of a plug-flow reactor under saturation, IFAC-PapersOnLine, vol.49, p.2016 ,
Spectral assignability for distributed parameter systems with unbounded scalar control ,
, SIAM J. Control Optim, vol.27, issue.1, pp.148-169, 1989.
Control theory of hyperbolic equations related to certain questions in harmonic analysis 24 and spectral theory, J. Math. Anal. Appl, vol.40, pp.336-368, 1972. ,
Canonical forms and spectral determination for a class of hyperbolic distributed parameter 26 control systems, J. Math. Anal. Appl, vol.62, issue.1, pp.186-225, 1978. ,
Boundary stabilization of a 1-D wave equation 28 with in-domain antidamping, SIAM J. Control Optim, vol.48, issue.6, pp.4014-4031, 2010. ,
Mathematical control theory, Texts in Applied Mathematics, vol.6 ,
, Deterministic finite-dimensional systems, 1998.
On spectrum distribution of completely controllable linear systems, SIAM J. Control Optim, vol.32, issue.6, pp.730-743, 1981. ,
Backstepping control for parabolic pdes with in-domain 34 actuation, American Control Conference (ACC), pp.2226-2231, 2012. ,
Rapid exponential feedback stabilization with unbounded control operators, SIAM J ,
, Control Optim, vol.43, issue.6, pp.2233-2244, 2005.
Rapid stabilization in a semigroup framework, SIAM J. Control Optim, vol.51, issue.5, p.2013 ,
URL : https://hal.archives-ouvertes.fr/hal-01272024
Backstepping design for parabolic systems with in-40 domain actuation and Robin boundary conditions, IFAC Proceedings Volumes, vol.47, pp.5175-5180, 2014. ,
Null controllability of a linearized Korteweg-de Vries equation by backstepping approach. 43 preprint, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01468750
Small-time local stabilization for a Korteweg-de Vries equation, Systems Control Lett, vol.45, pp.64-69, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01723178
Backstepping synthesis for feedback ,