Synthesis of switching rules for switched linear systems through randomized algorithms

In this paper, the design of a stabilizing switching rule for a switched linear system is considered. We first propose a probabilistic algorithm for a known nonconvex condition that employs a multiple Lyapunov function. We prove a probability-one convergence of the algorithm under a new notion of convergence. Then, to reduce its complexity, a modified version of the algorithm is developed. The results are illustrated using two-and three-dimensional systems with multiple switch states.