Data-driven stability analysis of switched affine systems

TL;DR

This paper develops data-driven methods for analyzing the stability and attractors of switched affine systems, connecting stability properties with joint spectral radius and providing probabilistic certificates based on sampled trajectories.

Contribution

It introduces novel probabilistic stability certificates for switched affine systems using limited data, extending existing theoretical results with practical sampling-based approaches.

Findings

Probabilistic stability certificates can be derived from finite trajectory samples.

The methods relate stability analysis to the joint spectral radius of system matrices.

Numerical examples demonstrate the effectiveness and limitations of the proposed conditions.

Abstract

We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact attractors, and the relations these problems have with the joint spectral radius of the set of matrices composing the linear part of the subsystems. Second, we tackle the problem of providing probabilistic certificates of stability along with the existence of forward invariant sets, assuming no knowledge on the system data but only observing a finite number of sampled trajectories. Some numerical examples illustrate the advantages and limits of the proposed conditions.