Sliding mode control of T–S fuzzy descriptor systems with time-delay

This paper is concerned with the problem of sliding mode control (SMC) of a class of Takagi–Sugeno (T–S) fuzzy descriptor system with time-delay. An integral-type sliding surface function is designed by taking the descriptor matrix into account, thus the resulting sliding mode dynamics is a full-order uncertain T–S fuzzy descriptor time-delay system. By the use of the delay partitioning technique, a delay-dependent criterion is established, which ensures the sliding mode dynamics to be regular, impulse-free and stable. Moreover, an SMC law is synthesized to guarantee the stability of the closed-loop system, and the proposed SMC law can drive the dynamics of controlled system into a designated sliding surface in finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theories.