Data Driven Stability Analysis of Black-box Switched Linear Systems
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.
Cite
@article{arxiv.1803.03687,
title = {Data Driven Stability Analysis of Black-box Switched Linear Systems},
author = {Joris Kenanian and Ayca Balkan and Raphael M. Jungers and Paulo Tabuada},
journal= {arXiv preprint arXiv:1803.03687},
year = {2018}
}