Stability and stabilization of fuzzy time-delay systems

In this paper, we consider the stability and stabilization of Takagi-Sugeno fuzzy time-delay systems. It is well-known that Takagi-Sugeno fuzzy systems approximate nonlinear systems and they can even describe a certain class of nonlinear systems exactly. On the other hand, time-delay systems appear in many practical systems and mathematical formulations. Thus Takagi-Sugeno fuzzy time-delay systems describe a wide class of nonlinear systems. For these fuzzy time-delay systems, we first make stability analysis and obtain sufficient conditions for the stability. Sufficient conditions we obtain here depend on the maximum value of time-delay and are given in linear matrix inequalities (LMFs). Next, we consider the stabilization problem. Based on the stability conditions, we obtain time-dependent sufficient conditions for the closed-loop system to be stable, and give a design method of stabilizing controllers. Furthermore, we consider the stability and stabilization for Takagi-Sugeno fuzzy neutral systems. Descriptor system approach is taken to analyze the stability and stabilization of fuzzy neutral systems. Similarly, we obtain time-dependent sufficient conditions for the stability of neutral systems. We also obtain sufficient conditions on the stabilization of neutral systems.