Robust Stabilization of Uncertain Fuzzy-Time-Delay Systems Using Sliding-Mode-Control Approach

Based on sliding-mode-control theory, we develop a fuzzy controller design method for a class of uncertain time-delay systems that can be represented by Takagi-Sugeno (T-S) fuzzy models. In terms of linear-matrix inequalities (LMIs), we derive a sufficient condition for the existence of stabilizing sliding-mode controllers. We show that the sliding-surface parameter matrix can be characterized in terms of the solution of the LMI-existence condition. Our LMI condition does not require stabilization of the pair of the state and input matrices. Thus, our method can be applied to a broad class of uncertain systems. We also give an LMI-based algorithm to design a switching feedback-control strategy so that a stable sliding motion is induced in finite time. Finally, we give a numerical-design example to show that our method can be better than the previous results.