Local Stabilization for Discrete-Time Fuzzy System With Guaranteed Resilience via Structural Relaxation

This article aims to investigate relaxed local stabilization for discrete-time Takagi-Sugeno fuzzy systems with structural relaxation under guaranteed resilience. To mitigate the conservatism and computational burden associated with conventional multiple summation-type approaches for exploiting high-degree membership information, a novel Lyapunov function and nonparallel distributed compensation (non-PDC) control law are developed within an augmented membership-quadratic framework, which relaxes the symmetry constraints on the intertemporal cross terms. To overcome the limitations of existing resilient stabilization methods that rely heavily on a user-defined hyperparameter, a matrix-type threshold condition is introduced, enhancing both practicality and numerical efficiency. Based on orthogonal complements, new structural relaxation lemmas within the membership-quadratic framework are proposed for guaranteeing resilient stabilization. Finally, the effectiveness and reduced conservatism of the proposed method are validated through benchmark examples, demonstrating its computational efficiency and improved performance compared to existing approaches.