Reachable set estimation and controller design for discrete‐time singularly perturbed systems with time‐varying delay
Guobao Liu, Shengyuan Xu, Wenhui Liu, Yu‐Ming Chu, Zhengqiang Zhang
Abstract
Abstract In this article, we study the reachable set estimation and controller design problems for a class of discrete time‐varying‐delay singularly perturbed systems. First, by constructing a ‐dependent Lyapunov–Krasovskii functional and using reciprocally convex inequality, delay‐dependent conditions are obtained to ensure the state of the system under zero initial conditions is contained by an ellipsoid for any singularly perturbed parameters below a given threshold. Second, by the method of designing a state‐feedback controller, sufficient conditions that the reachable set of the closed‐loop system can be included in a given ellipsoid are obtained for admissible singularly perturbed parameters. Finally, two examples are given to illustrate the effectiveness of the results.