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

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.

Automated summary

This paper addresses the region stability issues of switched discrete-time linear systems with multiple equilibrium points and all subsystems unstable. It introduces the concepts of region stability, globally asymptotic region stability, and region instability, and proposes sufficient conditions for these stability criteria under certain assumptions. The paper also designs an algorithm for globally asymptotic region stability based on the results obtained.