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Data-driven feedback stabilization of switched linear systems with probabilistic stability guarantees

This paper tackles the feedback stabilization of switched linear systems under arbitrary switching. We propose a data-driven approach which allows to compute a stabilizing static feedback using only a finite set of observations of trajectories without any knowledge of the dynamics. We assume that the switching signal is not observed, and as a consequence, we aim at solving a uniform stabilization problem in which the feedback is stabilizing for all possible switching sequences. In order to generalize the solution obtained from trajectories to the actual system, probabilistic guarantees are derived via geometric analysis in the spirit of scenario optimization. The performance of this approach is demonstrated on a few numerical examples.