Showing papers by "Jamal Daafouz published in 2002"
TL;DR: The approach followed in this paper looks at the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration and shows that the second condition is, in this case, less conservative.
Abstract: This paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete-time domain. The approach followed in this paper looks at the existence of a switched quadratic Lyapunov function to check asymptotic stability of the switched system under consideration. Two different linear matrix inequality-based conditions allow to check the existence of such a Lyapunov function. The first one is classical while the second is new and uses a slack variable, which makes it useful for design problems. These two conditions are proved to be equivalent for stability analysis. Investigating the static output feedback control problem, we show that the second condition is, in this case, less conservative. The reduction of the conservatism is illustrated by a numerical evaluation.
1,398 citations
TL;DR: In this article, a link between poly-quadratic stability and stability of arbitrary switching systems is established, and the necessary and sufficient condition of poly-quadratic stability proposed in Daafouz and Bernussou (2001) is shown to be immediately applicable to a class of switched control and observer design problems.
Abstract: In this paper, a link between poly-quadratic stability and stability of arbitrary switching systems is established. Polyquadratic stability aims to check asymptotic stability of a polytopic system by means of polytopic quadratic Lyapunov functions. The necessary and sufficient condition of poly-quadratic stability proposed in Daafouz and Bernussou (2001) is shown to be immediately applicable to a class of switched control and observer design problems. Chaos synchronization for which the transmitter is described by a piecewise linear map is presented as an application.
53 citations
10 Dec 2002
TL;DR: In this paper, robust output feedback control problem for switched discrete time systems is investigated and a switched dynamic output feedback law is found which stabilizes the switched closed loop system while satisfying a /spl gamma/-performance condition.
Abstract: In this paper, robust output feedback control problem for switched discrete time systems is investigated. For linear switched systems we look for a switched dynamic output feedback law which stabilizes the switched closed loop system while satisfying a /spl gamma/-performance condition. Design of such a control law is performed by solving LMI based conditions.
44 citations
TL;DR: This paper presents LQ decentralized pole location for singularly perturbed systems and shows that the LQ control problem with pole location in a sector can be solved using the LMI tool.
32 citations
TL;DR: This paper considers global chaos synchronization as an observer design problem using a poly-quadratic stability concept based on the use of parameter-dependent Lyapunov functions to check stability and leads to a reduction of the restricitions relative to conditions involving a unique LyAPunov function.
27 citations
TL;DR: In this paper, a link between poly-quadratic stability and stability of a class of hybrid systems is established, and the necessary and sufficient condition of poly-quadratic stability proposed in Daafouz and Bernussou (2001) is shown to be immediately applicable to a subclass of switched control and observer design problems.
9 citations
TL;DR: In this paper, the authors present a systematic framework for the design of gain scheduled observer based controllers for affine linear parameter-varying (LPV) systems based on parameter-dependent Lyapunov functions.
3 citations
08 May 2002
TL;DR: The proposed design attempts to enlarge the class of nonlinear systems for which an observer can be synthesized by solving a set of linear matrix inequalities derived from recent results of poly-quadratic stability.
Abstract: The design of nonlinear systems observer with global convergence when nonlinearities are not available in real time is proposed. A support vector machine is chosen in order to estimate the nonlinearities from the only available information, that is the output of the system, in a unified framework for both piecewise linear systems or nonlinear systems. The global convergence of the observer is ensured by a polytopic decomposition of the system state representation which enables one to compute the gain of the observer by solving a set of linear matrix inequalities derived from recent results of poly-quadratic stability. The proposed design attempts to enlarge the class of nonlinear systems for which an observer can be synthesized.
1 citations
10 Dec 2002
TL;DR: It is shown that information recovery requires an input independent global synchronization (IIGS) of the drive and response systems and a special lyapunov approach ensures the global convergence of the state reconstruction error.
Abstract: A piecewise linear system is presented in order to generate the chaotic motion . It is shown that information recovery requires an input independent global synchronization (IIGS) of the drive and response systems. Synchronization problem is tackled by first, a partial pole placement technique which enables the equation governing the state reconstruction error to become input independent. Secondly a special lyapunov approach ensures the global convergence of the state reconstruction error.
1 citations
TL;DR: In this paper, non-stationary quadratic Lyapunov functions are derived for synthesis in a poly-quadratic LQF concept, which avoids in a large extent the conservatism linked with the classical single-LQF approach, and the results are extended to cope with two particular problems: performance analysis and synthesis problem as well as state feedback design.