Passivity analysis for uncertain T-S Fuzzy Descriptor System with time-delay via Sliding Mode Control

In this paper the problem of passivity of a class of uncertain T-S fuzzy descriptor time-delay systems is analyzed. We consider the design of an integral-type sliding surface function such that the resulting sliding mode dynamics is a full-order uncertain T-S fuzzy descriptor time-delay system. A delay-dependent sufficient condition is proposed in terms of linear matrix inequality (LMI), which guarantees the sliding mode dynamics to be admissible and robustly passive. Furthermore, a SMC law is synthesized to ensure the dynamics of controlled system into a predefined switching surface in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.