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

TL;DR

This paper proves that for stable subsystems, a linear state feedback switching rule can be designed to globally stabilize switched nonlinear systems around a switched equilibrium point, simplifying previous nonlinear approaches.

Contribution

It demonstrates that the switching threshold can be linear if each subsystem is stable, extending prior nonlinear stabilization methods to linear thresholds.

Findings

Linear switching threshold is sufficient for stabilization.

Previous nonlinear thresholds can be replaced by linear ones under stability.

The method applies to affine switched systems around a switched equilibrium.

Abstract

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-Peleties-DeCarlo (1998) for linear systems, Bolzern-Spinelli (2004) offered a design of a state feedback switching rule that is capable to stabilize an affine 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 are stable.