During the past several years, there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems. This paper aims to briefly survey recent results in this field. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After a brief review of the stability analysis under restricted switching and the multiple Lyapunov function theory, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. Then the switching stabilizability problem is investigated, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature. A necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here.

Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results

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.

Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach

Networked control systems (NCSs) have, in recent years, brought many innovative impacts to control systems. However, great challenges are also met due to the network-induced imperfections. Such network-induced imperfections are handled as various constraints, which should appropriately be considered in the analysis and design of NCSs. In this paper, the main methodologies suggested in the literature to cope with typical network-induced constraints, namely time delays, packet losses and disorder, time-varying transmission intervals, competition of multiple nodes accessing networks, and data quantization are surveyed; the constraints suggested in the literature on the first two types of constraints are updated in different categorizing ways; and those on the latter three types of constraints are extended.

Network-Induced Constraints in Networked Control Systems—A Survey

In this paper, the stability and stabilization problems for a class of switched linear systems with mode-dependent average dwell time (MDADT) are investigated in both continuous-time and discrete-time contexts. The proposed switching law is more applicable in practice than the average dwell time (ADT) switching in which each mode in the underlying system has its own ADT. The stability criteria for switched systems with MDADT in nonlinear setting are firstly derived, by which the conditions for stability and stabilization for linear systems are also presented. A numerical example is given to show the validity and potential of the developed techniques.

Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time

There are many communication imperfections in networked control systems (NCS) such as varying transmission delays, varying sampling/transmission intervals, packet loss, communication constraints and quantization effects. Most of the available literature on NCS focuses on only some of these aspects, while ignoring the others. In this paper we present a general framework that incorporates communication constraints, varying transmission intervals and varying delays. Based on a newly developed NCS model including all these network phenomena, we will provide an explicit construction of a continuum of Lyapunov functions. Based on this continuum of Lyapunov functions we will derive bounds on the maximally allowable transmission interval (MATI) and the maximally allowable delay (MAD) that guarantee stability of the NCS in the presence of communication constraints. The developed theory includes recently improved results for delay-free NCS as a special case. After considering stability, we also study semi-global practical stability (under weaker conditions) and performance of the NCS in terms of Lp gains from disturbance inputs to controlled outputs. The developed results lead to tradeoff curves between MATI, MAD and performance gains that depend on the used protocol. These tradeoff curves provide quantitative information that supports the network designer when selecting appropriate networks and protocols guaranteeing stability and a desirable level of performance, while being robust to specified variations in delays and transmission intervals. The complete design procedure will be illustrated using a benchmark example.

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Networked Control Systems With Communication Constraints: Tradeoffs Between Transmission Intervals, Delays and Performance

Dans cet article, a partir d’une relecture de la consistance des systemes commutes lineaires, la propriete de consistance pour les systemes non-lineaires de type Lur’e commutes a temps discret est etudiee. Une discussion montre qu’il faut considerer le plus petit majorant quadratique possible de la performance au lieu de la valeur optimale elle-meme (qui coincident dans le cadre lineaire) pour permettre l’extension. Un probleme d’optimisation sous contraintes LMI est propose pour obtenir une strategie de type min-switching satisfaisant la consistance en non-lineaire. Dans un second temps, cette contribution est utilisee pour la synthese d’un controleur a donnees echantillonnees avec un echantillonnage non uniforme. Un exemple numerique est alors propose pour mettre en evidence les apports de ces resultats.

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Consistance des systèmes de Lur’e commutés. Application à la synthèse de commande numérique avec un échantillonnage non uniforme

Optimistic planning for control of hybrid-input nonlinear systems

On persistent excitations for the identification of switched linear dynamical systems over finite fields

Delay-dependent sampled-data control of LTI systems

In this paper, we present properties of dynamical systems and their use for cryptographical applications. In particular, we study the relationship with the self-synchronizing stream ciphers from a structural point of view. A special class of dynamical systems, namely the piecewise linear systems, are then considered.

https://hal.archives-ouvertes.fr/hal-00331835/document

Jamal Daafouz

Papers

Consistance des systèmes de Lur’e commutés. Application à la synthèse de commande numérique avec un échantillonnage non uniforme

Optimistic planning for control of hybrid-input nonlinear systems

On persistent excitations for the identification of switched linear dynamical systems over finite fields

Delay-dependent sampled-data control of LTI systems

Designing Self-Synchronizing Stream Ciphers with Flat Dynamical Systems