Controllability of the linear switched dynamical systems of the special type (original) (raw)
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Hybrid systems are dynamic systems that arise out of the interaction of continuous state dynamics and discrete state dynamics. Switched systems, which are a type of hybrid system, have been given much attention by control systems research over the past decade. Problems with the controllability, observability, converseability and stabilizability of switched systems have always been discussed. In this paper, the trend in research regarding the stability of switched systems will be investigated. Then the variety of methods that have been discovered by researchers for stabilizing switched linear systems with arbitrary switching will be discussed in detail.
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In this paper we consider the controllability problem for discrete-time linear switched systems. The problem consists of finding a control signal that steers any initial condition to a given final state regardless of the switching signal. In the paper a necessary and sufficient conditions for this type of controllability are presented. Moreover, we consider problems of controllability from zero initial condition and to zero final state.
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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.
Bulletin of The Polish Academy of Sciences-technical Sciences, 2015
In this paper the controllability problem for discrete-time linear switched systems is considered. The main goal is to find a control signal that steers any initial state to a given final state independently of the switching signal. In the paper, it is assumed that there are some constraints posed on the switching signal. Moreover, we present a necessary and sufficient conditions of some kinds of controllability. Three types of controllability, namely: from zero initial state to any final state, from any initial state to zero final state and from any initial state to any final state are considered. Finally, three illustrative examples are shown.
Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results
IEEE Transactions on Automatic Control, 2009
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.
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In this paper, the structural controllability of switched linear systems is investigated. The structural controllability is a generalization of the traditional controllability concept for dynamical systems, and purely based on the graphic topologies among state and input vertices. First, two kinds of graphic representations of switched linear systems are proposed. Second, graph theory based necessary and sufficient characterizations of the structural controllability for switched linear systems are presented. Finally, the paper concludes with illustrative examples and discussions on the results and future work.
Stability analysis for a class of nonlinear switched systems
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2000
In the present paper, we study several qualitative properties of a class of nonlinear switched systems under certain switching laws. First, we show that if all the subsystems are linear time-invariant and the system matrices are commutative componentwise and stable, then the entire switched system is globally exponentially stable under arbitrary switching laws. Next, we study the above linear switched systems with certain nonlinear perturbations, which can be either vanishing or non-vanishing. Under reasonable assumptions, global exponential stability is established for these systems. We further study the stability and instability properties, under certain switching laws, for switched systems with commutative subsystem matrices that may be unstable. Results for both continuous-time and discrete-time cases are presented.