Region stability of switched DTL systems with all subsystems unstable and multi-equilibria

Abstract

This paper addresses region stability issues of switched discrete-time linear (DTL) systems with all subsystems unstable and multiple equilibrium points (ASU-MEPs). The new concepts of region stability (RS), globally asymptotical region stability (GARS), and region instability (RIS) are defined for the switched DTL systems with ASU-MEPs. Based on these concepts introduced, this paper proposes several sufficient conditions of RS, GARS, and RIS for switched DTL systems with ASU-MEPs under the case as follows. Each subsystem of such kind of switched systems owns a single equilibrium point (SEP). There are at least two different subsystems' equilibrium points. The stability criteria obtained in this paper are with respect to a suitable region that contains all the subsystems' MEPs. Moreover, such kind of stability criteria is an extension of the classical eigenvalue stability criterion of non-switching DTL systems with SEP. By means of the GARS result, this paper designs an algorithm of globally asymptotical region stability for switched DTL systems with ASU-MEPs. The above results are applied to a commodity-selling market network.