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

Abstract

Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.