Memory Sampled-Data Controller Design for Interval Type-2 Fuzzy Systems via Polynomial-Type Lyapunov–Krasovskii Functional

Abstract

This study deals with the investigation of the interval type-2 (IT2) fuzzy sampled-data (SD) stabilization problem based on nonlinearities and parameter uncertainties. For the first time, a memory SD control design involving a known signal transmission delay is adapted to address the stabilization problem for IT2 fuzzy systems. New polynomial-type Lyapunov–Krasovskii functionals (LKFs) associated with the state of constant signal transmission delay are introduced to achieve less conservative stability results. To bound the derivative of such LKFs, the Jacobi–Bessel inequality is introduced. Due to this, improved delay-dependent sufficient conditions can be obtained relating to set of linear matrix inequalities (LMIs). Thus, by solving LMIs using the LMI solver in MATLAB, the closed-loop system can be stabilized. The proposed method is verified in the simulation results with a nonlinear permanent-magnet vernier generator (PMVG)-based wind energy model and a Rossler model. Also, the applicability and superiority of the derived sufficient conditions are proved when compared with the existing results.