Yet another stability condition for switched nonlinear systems

TL;DR

This paper introduces a new stability condition for continuous-time switched nonlinear systems, using multiple Lyapunov-like functions to ensure input/output-to-state stability under specific switching restrictions.

Contribution

It provides a novel stability criterion for switched nonlinear systems with unstable dynamics, extending existing results by incorporating input/output considerations and dwell-time restrictions.

Findings

Identifies a class of switching signals that preserve stability.

Ensures input-to-state stability under switching restrictions.

Extends stability analysis to systems with unstable dynamics.

Abstract

This paper deals with input/output-to-state stability (IOSS) of continuous-time switched nonlinear systems. Given a family of systems, possibly containing unstable dynamics, and a set of restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems, we identify a class of switching signals that obeys these restrictions and preserves stability of the resulting switched system. The primary apparatus for our analysis is multiple Lyapunov-like functions. Input-to-state stability (ISS) and global asymptotic stability (GAS) of switched systems under pre-specified restrictions on switching signals fall as special cases of our results when no outputs (resp., also inputs) are considered.