Probabilistic design of switched systems

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 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. That is, the algorithm can solve both of the feasible and the infeasible problems, which is demonstrated in numerical examples.