Design of memory-based adaptive integral sliding-mode controller for fractional-order T-S fuzzy systems and its applications

Abstract

This study investigates the passivity analysis of fractional-order Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and nonlinear perturbations under an adaptive integral sliding mode control (AISMC) methodology. To better accommodate the features of the T-S fuzzy dynamical model, a novel fractional-order memory-based integral-type sliding manifold function is defined, which is different from the existing sliding manifold function. With the help of Caputo fractional-order derivative properties and quadratic Lyapunov functional, some linear matrix inequality (LMI)-based sufficient criteria are derived to ensure the asymptotic stability conditions of resulting sliding mode dynamics with passive performance index. Besides that, an adaptive sliding mode control law is designed for the addressed systems to guarantee the system state variables onto the predefined integral sliding manifold. Finally, the effectiveness of the proposed controller is validated based on derived sufficient conditions with two practical models, such as fractional-order interconnected power systems and fractional-order permanent-magnet synchronous generator (PMSG) model, respectively.