Estimation and synthesis of reachable set for discrete-time periodic systems

This paper is concerned with the problems of reachable set estimation and synthesis for discrete‐time periodic systems under bounded peak disturbances. For the reachable set estimation problem, the lifting approach and the pseudo‐periodic Lyapunov function approach are utilized to determine the bounding ellipsoids for the reachable set. By using the lifting approach, the periodic system is transformed into several time‐invariant systems; then, the bounding ellipsoids are determined through the transformed time‐invariant systems. By applying the pseudo‐periodic Lyapunov function approach, the bounding ellipsoids are determined through the original periodic system directly. Genetic algorithm is adopted in the pseudo‐periodic Lyapunov function approach to search for the optimal value of the decision variables. Moreover, based on the reachable set estimation results, state‐feedback controllers are designed for manipulating the reachable set. Finally, numerical examples are presented to verify the effectiveness of the theoretical findings