Asymmetric Lyapunov–Krasovskii Functional Method for Reachable Set Estimation and Controller Design of Singular Nonlinear Systems With Time‐Varying Delays

ABSTRACT In this article, we investigate the problems of reachable set estimation (ReSE) and controller design for a class of singular nonlinear systems with time‐varying delays (SNS‐TVDs). To this end, a novel asymmetric Lyapunov–Krasovskii functional is constructed, together with zero‐type free matrix equations and several recently developed fundamental lemmas. Based on these tools, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to ensure the admissibility of the considered system and the existence of an ellipsoidal bound enclosing all possible system trajectories under bounded exogenous disturbances. Furthermore, a state‐feedback controller is designed to guarantee that the reachable set of the resulting closed‐loop system is confined within a prescribed ellipsoid. Finally, numerical examples and simulation results are provided to demonstrate the effectiveness of the proposed approach.