Data Driven Stability Analysis of Black-box Switched Linear Systems

TL;DR

This paper develops a probabilistic framework to assess the stability of black-box switched linear systems using finite trajectory snapshots, balancing confidence levels with the amount of data.

Contribution

It introduces a method to provide stability guarantees for unknown switched systems based on limited observational data, utilizing geometrical and optimization techniques.

Findings

Provides explicit stability guarantees from finite data

Establishes a trade-off between confidence level and data quantity

Uses joint spectral radius in stability analysis

Abstract

Can we conclude the stability of an unknown dynamical system from the knowledge of a finite number of snapshots of trajectories? We tackle this black-box problem for switched linear systems. We show that, for any given random set of observations, one can give probabilistic stability guarantees. The probabilistic nature of these guarantees implies a trade-off between their quality and the desired level of confidence. We provide an explicit way of computing the best stability-like guarantee, as a function of both the number of observations and the required level of confidence. Our proof techniques rely on geometrical analysis, chance-constrained optimization, and stability analysis tools for switched systems, including the joint spectral radius.