Learning stability guarantees for constrained switching linear systems from noisy observations

TL;DR

This paper introduces a data-driven Lyapunov-based method to provide probabilistic stability guarantees for constrained switching linear systems using noisy observational data, applicable even with partial state observations.

Contribution

It develops a novel approach to derive stability guarantees from finite noisy data for constrained switching systems, including cases with partial state observations.

Findings

Provides chance-constrained stability bounds from sampled trajectories.

Extends stability guarantees to systems with only partial state observations.

Introduces a new upper bound relevant for model-based stability analysis.

Abstract

We present a data-driven framework based on Lyapunov theory to provide stability guarantees for a family of hybrid systems. In particular, we are interested in the asymptotic stability of switching linear systems whose switching sequence is constrained by labeled graphs, namely constrained switching linear systems. In order to do so, we provide chance-constrained bounds on stability guarantees, that can be obtained from a finite number of noisy observations. We first present a method providing stability guarantees from sampled trajectories in the hybrid state-space of the system. We then study the harder situation where one only observes the continuous part of the hybrid states. We show that in this case, one may still obtain formal chance-constrained stability guarantees. For this latter result we provide a new upper bound of general interest, also for model-based stability analysis