Learning stability of partially observed switched linear systems

TL;DR

This paper introduces a data-driven method for assessing the stability of partially observed switched linear systems using output data, providing a probabilistic bound on the joint spectral radius estimate.

Contribution

It presents a novel output-based stability analysis algorithm that estimates the joint spectral radius without requiring internal state knowledge.

Findings

Algorithm effectively estimates stability from output data.

Provides probabilistic error bounds on the joint spectral radius estimate.

Applicable to cyber-physical systems with partial observability.

Abstract

This paper deals with learning stability of partially observed switched linear systems under arbitrary switching. Such systems are widely used to describe cyber-physical systems which arise by combining physical systems with digital components. In many real-world applications, the internal states cannot be observed directly. It is thus more realistic to conduct system analysis using the outputs of the system. Stability is one of the most frequent requirement for safety and robustness of cyber-physical systems. Existing methods for analyzing stability of switched linear systems often require the knowledge of the parameters and/or all the states of the underlying system. In this paper, we propose an algorithm for deciding stability of switched linear systems under arbitrary switching based purely on observed output data. The proposed algorithm essentially relies on an output-based Lyapunov stability framework and returns an estimate of the joint spectral radius (JSR). We also prove a probably approximately correct error bound on the quality of the estimate of the JSR from the perspective of statistical learning theory.