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Kybernetika 46 no. 5, 870-889, 2010

Finite-time boundedness and stabilization of switched linear systems

Haibo Du, Xiangze Lin and Shihua Li

Abstract:

In this paper, finite-time boundedness and stabilization problems for a class of switched linear systems with time-varying exogenous disturbances are studied. Firstly, the concepts of finite-time stability and finite-time boundedness are extended to switched linear systems. Then, based on matrix inequalities, some sufficient conditions under which the switched linear systems are finite-time bounded and uniformly finite-time bounded are given. Moreover, to solve the finite-time stabilization problem, stabilizing controllers and a class of switching signals are designed. The main results are proven by using the multiple Lyapunov-like functions method, the single Lyapunov-like function method and the common Lyapunov-like function method, respectively. Finally, three examples are employed to verify the efficiency of the proposed methods.

Keywords:

switched linear systems, finite-time boundedness, multiple Lyapunov-like functions, single Lyapunov-like function, common Lyapunov-like function

Classification:

93A14, 93C10, 93D15, 93D21

paper.pdf

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