SMC for Discrete 2-D Markov Switching Systems: Genetic Algorithm

The sliding mode control (SMC) strategy based on genetic algorithm is proposed for discrete two-dimensional (2-D) Markov switching systems with the Roesser model. By means of common 2-D sliding surface, the 2-D SMC law is designed for the underlying system. According to Lyapunov stability criteria, sufficient conditions are established for the asymptotic mean-square stability of the underlying 2-D Markov switching systems and the reachability of the sliding region is guaranteed. Utilizing an iteration optimizing algorithm, an effective SMC strategy under genetic algorithm is constructed to minimize the sliding region by searching an ideal sliding gain. Finally, the applicability of the proposed 2-D SMC strategy is verified through an example.