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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.