T-S fuzzy design for nonlinear state-delayed descriptor system via sliding mode control

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 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, a 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 a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theories.