Guaranteed Cost Control Strategy for Stabilizing Discrete-Time TS Fuzzy State-Delayed Systems

The guaranteed cost control challenge for discrete-time nonlinear systems that include time-varying delays is the central topic of this paper. We propose a novel synthesis of state feedback controllers to achieve asymptotic stability and ensure a satisfactory level of performance in the closed-loop system. To address the time-varying parameters and control, we leverage the Takagi–Sugeno (TS) fuzzy formalism, the Lyapunov–Krasovskii functional (LKF) framework, and free-weighting matrices. Furthermore, we establish novel delay-dependent linear matrix inequalities (LMIs) that guarantee the stability of the closed-loop system. To illustrate the benefits of our approach and compare it with existing literature works, we provide numerical examples. These examples showcase the practical application and advantages of the suggested approach.