Learning stability guarantees for constrained switching linear systems from noisy observations
Adrien Banse, Zheming Wang, and Raphaël M. Jungers
Nonlinear Analysis: Hybrid Systems 2024
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 observations with bounded noise. 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.
Learning stability guarantees for data-driven constrained switching linear systems25th International Symposium on Mathematical Theory of Networks and Systems (Bayreuth, Germany) 2022
