Data-Driven Stability Analysis of Switched Linear Systems Using Adaptive Sampling

In the realm of system analysis, data-driven methods have gained a lot of attention in recent years. We introduce a new innovative approach for the data-driven stability analysis of switched linear systems which is adaptive sampling. Our aim is to address limitations of existing approaches, in particular, the fact that these methods suffer from ill-conditioning of the optimal Lyapunov function, which is a direct consequence of the way the data is collected by sampling uniformly the state space. Our adaptive-sampling approach consists in a two-step procedure, in which an optimal sampling distribution is estimated in the first step from data collected with a non-optimal distribution, and then, in the second step, new data points are sampled according to the identified distribution to establish the final probabilistic guarantee for the convergence rate of the system. Numerical experiments show the efficiency of our approach, namely, in terms of the total number of data points needed to guarantee stability of the system with given confidence. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)