Author
Lionel Rosier
Other affiliations: French Institute for Research in Computer Science and Automation, Nancy-Université, Mines ParisTech ...read more
Bio: Lionel Rosier is an academic researcher from PSL Research University. The author has contributed to research in topics: Controllability & Heat equation. The author has an hindex of 29, co-authored 126 publications receiving 3956 citations. Previous affiliations of Lionel Rosier include French Institute for Research in Computer Science and Automation & Nancy-Université.
Papers published on a yearly basis
Papers
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01 Jan 2001
TL;DR: Differential equations and differential inclusions of strict Liapunov functions have been studied in this paper for time invariant systems and time varying systems, as well as generalized derivatives.
Abstract: Differential equations.- Time invariant systems.- Time varying systems.- Differential inclusions.- Additional properties of strict Liapunov functions.- Monotonicity and generalized derivatives.
888 citations
TL;DR: In this article, a construction of a homogeneous Lyapunov function P associated with a system of differential equations J = f(x), x ~ R ~ (n > 1), under the hypotheses: (1) f ~ C(R n, ~) vanishes at x = 0 and is homogeneous; (2) the zero solution of this system is locally asymptotically stable.
720 citations
TL;DR: In this paper, the exact boundary controllability of linear and nonlinear Korteweg-de Vries equations on bounded domains with various boundary conditions is studied, for sufficiently small initial and final states.
Abstract: The exact boundary controllability of linear and nonlinear Korteweg-de Vries equation on bounded domains with various boundary conditions is studied. When boundary conditions bear on spatial derivatives up to order 2, the exact controllability result by Russell-Zhang is directly proved by means of Hilbert Uniqueness Method. When only the first spatial derivative at the right endpoint is assumed to be controlled, a quite different analysis shows that exact controllability holds too. From this last result we derive the exact boundary controllability for nonlinear KdV equation on bounded domains, for sufficiently small initial and final states.
339 citations
TL;DR: An overall review of the results obtained so far in the study of the control and stabilization of the KdV equation with an emphasis on its recent progresses is given.
Abstract: The study of the control and stabilization of the KdV equation began with the work of Russell and Zhang in late 1980s. Both exact control and stabilization problems have been intensively studied since then and significant progresses have been made due to many people's hard work and contributions. In this article, the authors intend to give an overall review of the results obtained so far in the study but with an emphasis on its recent progresses. A list of open problems is also provided for further investigation.
135 citations
TL;DR: The global exponential stability is obtained whatever the location where the damping is active, confirming positively a conjecture of Perla Menzala, Vasconcellos, and Zuazua.
Abstract: This paper is concerned with the internal stabilization of the generalized Korteweg--de Vries equation on a bounded domain. The global well-posedness and the exponential stability are investigated when the exponent in the nonlinear term ranges over the interval [1,4). The global exponential stability is obtained whatever the location where the damping is active, confirming positively a conjecture of Perla Menzala, Vasconcellos, and Zuazua [Quart. Appl. Math., 60 (2002), pp. 111-129].
134 citations
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TL;DR: In this article, the authors proposed arbitrary-order robust exact differentiators with finite-time convergence, which can be used to keep accurate a given constraint and feature theoretically-infinite-frequency switching.
Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...
2,954 citations
01 Jan 2003
2,810 citations
1,620 citations
TL;DR: This work addresses the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.
Abstract: We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.
1,349 citations