A linear state feedback switching rule for global stabilization of switched nonlinear systems about a nonequilibrium point

摘要

A switched equilibrium of a switched system of two subsystems is a such a point where the vector fields of the two subsystems point strictly towards one another. Using the concept of stable convex combination that was developed by Wicks et al. (1998) for linear homogeneous systems, Bolzern and Spinelli (2004) offered a design of a state feedback switching rule that is capable to stabilize a linear nonhomogeneous switched system to any switched equilibrium. The state feedback switching rule of Bolzern-Spinelli gives a nonlinear (quadratic) switching threshold passing through the switched equilibrium. In this paper we prove that the switching threshold (i.e. the associated switching rule) can be chosen linear, if each of the subsystems of the switched system under consideration is globally asymptotically stable. (C) 2019 European Control Association. Published by Elsevier Ltd. All rights reserved.