Design of sampled-data controller for T–S fuzzy system with the refined fractional delayed-state and its applications

Abstract

The paper is concerned with the development of a sampled-data (SD) controller designed for Takagi–Sugeno (T–S) fuzzy systems. A key highlight is the incorporation of a refined fractional delayed-state into this control approach. The primary aim is to establish criteria for system stabilization, thereby ensuring the asymptotic stability of the considered systems. This objective is pursued within the framework of the newly designed control methodology. The core contribution of work explains in the introduction of an innovative Lyapunov–Krasovskii functional (LKF) tailored to T–S fuzzy systems. This novel approach capitalizes on the efficacy of sampling intervals. The LKF design takes advantage of variable attributes tied to the real sampling pattern, effectively reducing the conservatism of the outcomes. Moreover, the paper introduces a sophisticated fractional delayed-state concept, which plays a pivotal role in shaping a modified looped functional-based LKF. The stability criteria are then formulated through the utilization of linear matrix inequalities (LMIs) and integral inequalities. These criteria perform dynamic part in establishing the asymptotic stability of considered systems when subjected to the designed control approach.