Observer-Based Fuzzy Integral Sliding Mode Control For Nonlinear Descriptor Systems

Abstract

This paper investigates observer-based stabilization for nonlinear descriptor systems using a fuzzy integral sliding mode control approach. Observer-based integral sliding mode control strategies for the Takagi–Sugeno (T–S) fuzzy descriptor systems are developed. A two-step design approach is first developed to obtain the observer gains and coefficients in the switching function using linear matrix inequalities (LMIs), and the results are used to facilitate the development of a single-step design approach, which is seen to be convenient but introduces some conservatism in the design. The potential application to a class of mechanical systems is also considered. Since the descriptor system representation of mechanical systems is adopted, it is shown that in contrast to the existing fuzzy sliding mode control methods based on the normal system representation, the resulting T-S fuzzy system does not contain different input matrices for each local subsystem and the required number of fuzzy rules is consequently markedly reduced. Finally, the balancing problem of a pendulum on a car is numerically simulated to demonstrate the effectiveness of the proposed method.