Fuzzy Reduced-Order Compensator-Based Stabilization for Interconnected Descriptor Systems via Integral Sliding Modes

Abstract

This paper investigates the integral sliding mode control problem of T–S fuzzy interconnected descriptor system based on a reduced-order compensator. A canonical equivalent form for T–S fuzzy interconnected descriptor system is first introduced to facilitate the reduced-order compensator design. In terms of the measurable output variables of the T–S fuzzy interconnected descriptor system and the state variables of the proposed reduced-order compensator, an integral sliding mode control scheme is then developed for the T–S fuzzy interconnected descriptor system. The sliding motion is defined in the augmented space formed by the state variables of the original T–S fuzzy interconnected descriptor system and the resulting error system. It is shown that the designing parameters in the switching function can be simultaneously solved and the original T–S fuzzy interconnected descriptor system has no requirement to be relative degree one. Since the estimate error is bounded by an auxiliary dynamical system, when ideal sliding mode occurs, the resulting closed-loop system is asymptotically stable rather than uniformly ultimately bounded. Finally, a double-inverted pendulum system and a ball and beam system are numerically simulated to demonstrate the effectiveness and merits of the method proposed.