Finite-time stability and finite-time boundedness for switched systems with sector bounded nonlinearities

A switched system with sector bounded nonlinearities is a precisely unified model to describe many kinds of practical systems. However, up to now, only Lyapunov asymptotically stability of the system has been discussed. Moreover, the existing results of stability analysis and controller design for this kind of systems are under some conservative assumptions. In this paper, finite-time stability and finite-time boundedness for switched systems with sector bounded nonlinearities are studied. Sufficient conditions which guarantee the systems finite-time stable or finite-time bounded are presented. These conditions are given in terms of linear matrix inequalities. Average dwell time of switching signals is also given such that the switched nonlinear systems are finite-time bounded or finite-time stable. Detail proofs are accomplished by using multiple Lyapunov-like functions.

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