Robust Adaptive Sliding Mode Observer Design for T-S Fuzzy Descriptor Systems With Time-Varying Delay

This paper addresses the problems of robust adaptive sliding mode observer (SMO) design and SMO-based sliding mode control (SMC) for T-S fuzzy descriptor systems with time-varying delay. Until now, there are a few results about the adaptive SMO design problem and adaptive SMO-based SMC for T-S fuzzy descriptor systems with time-varying delay. Therefore, we are motivated to study this issue. First, two integral-type sliding surfaces, which involve the SMO gain matrix, are constructed for the error system and the SMO system, respectively. Then, some delay-dependent sufficient conditions are established, such that the sliding motions are robustly admissible with H∞ performance. New adaptive sliding mode controllers, which need not to use the assumption that the fast subsystem of descriptor system is observable, are synthesized for the error system and the SMO system, such that the reachability conditions can be guaranteed. In addition, the adaptive control strategy is applied to estimate the unknown parameters. Finally, simulation examples are discussed to show the effectiveness of our approach.