A randomized algorithm for the stabilization of switched nonlinear systems under restricted switching

TL;DR

This paper introduces a randomized algorithm for designing switching signals that ensure input/output-to-state stability in switched nonlinear systems, respecting specific switching restrictions and dwell times.

Contribution

It presents a novel randomized algorithm for constructing stabilizing switching signals under restricted switching conditions in discrete-time nonlinear systems.

Findings

The algorithm guarantees stability with high probability.

It extends previous probabilistic stability results to nonlinear systems.

Conditions on subsystems and switching restrictions ensure stability.

Abstract

This paper deals with input/output-to-state stability (IOSS) of switched nonlinear systems in the discrete-time setting. We present an algorithm to construct periodic switching signals that obey pre-specified restrictions on admissible switches between the subsystems and admissible dwell times on the subsystems, and identify sufficient conditions on the individual subsystems, the admissible switches and admissible dwell times under which a switching signal obtained from our algorithm preserves stability of a switched system with overwhelming probability. We recover our earlier result on probabilistic techniques for the design of switching signals that preserve global asymptotic stability of switched linear systems under sufficient conditions on the properties of the individual subsystems and the admissible dwell times on the subsystems.