Learning stability guarantees for data-driven constrained switching linear systems

TL;DR

This paper introduces a data-driven method to analyze the stability of constrained switching linear systems with unknown dynamics, using finite samples to construct Lyapunov functions and probabilistic guarantees.

Contribution

It generalizes existing stability analysis to systems with automaton-constrained switching, providing a sampling-based approach with bounds based on automaton entropy.

Findings

Finite samples suffice to approximate Lyapunov functions.

Automaton entropy bounds the required sample size.

Probabilistic stability guarantees are established.

Abstract

We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic stability guarantees based on data harvested from observations of the system. By generalizing previous results on arbitrary switching linear systems, we show that, by sampling a finite number of observations, we are able to construct an approximate Lyapunov function for the underlying system. Moreover, we show that the entropy of the language accepted by the automaton allows to bound the number of samples needed in order to reach some pre-specified accuracy.