Finite-time stability of set switched systems with non-instantaneous impulses

Abstract

In this paper, we discuss the finite-time stability of set switched systems with non-instantaneous impulses which consist of stable and unstable subsystems through introducing a revised mode-dependent average dwell time method. By designing time-dependent switching law and using the multiple Lyapunov-like functions method, the finite-time stability criteria of set switched systems with non-instantaneous impulses are given. Sufficient conditions which guarantee the finite-time boundedness of the switched systems with time-varying exogenous disturbances are also given. In our switching design strategy, slow switching and fast switching are, respectively, used among stable subsystems and unstable subsystems. The criteria obtained for the switched linear systems are all provided in terms of a set of linear matrix inequalities. Numerical examples are employed to verify the efficiency of the proposed method.

Keywords

• switched system
• set-valued
• non-instantaneous impulses
• finite-time stability
• finite-time boundedness