Stability and Stabilization of a Class of Multimode Linear Discrete-Time Systems With Polytopic Uncertainties

In this paper, the problems of stability and stabilization of a class of multimode systems, which are switched linear discrete-time systems with polytopic uncertainties, are investigated. Two types of switching, including fast and slow switchings, among the modes of systems are considered. The construction of multiple parameter-dependent quadratic Lyapunov-like functions is invoked, by which the stability and stabilization conditions are derived and formulated in terms of a set of linear matrix inequalities. The case of switched systems under fast switching, i.e., arbitrary switching is first studied, and the corresponding results are extended to the case of slow switching, i.e., average dwell time switching. The less conservativeness of the obtained results is illustrated by numerical examples. The applicability and effectiveness of the theoretical findings are also verified by a two-mass-spring mechanical system.