Probabilistic Design of Switched Systems

Abstract

Synthesis of stabilizing state-dependent switching rules is considered for multi-modal systems. The synthesis is recast as a problem which is to find a multiple-Lyapunov function, through the problem is not convex in general. In order to cope with this difficulty, a randomized algorithm is proposed, which is based on the stochastic ellipsoid method and a branching. The algorithm always stops in a finite number of iterations. Then, it gives a probabilistic solution with a prescribed confidence or says that the solution set is too small to be found in a deterministic sense. Although computational complexity of the algorithm is an exponential function of the problem size due to branching, numerical examples show that the algorithm solves several problems with moderate size.