Linear control and parallel distributed fuzzy control design for T-S fuzzy time-delay system

This paper studies the stabilization problem for T-S fuzzy systems with time delay. Based on Lyapunov criterion and Razumikhin theorem, two types of stabilizing controller are designed. One is the linear state feedback controller and the other is the parallel distributed fuzzy controller (PDFC). For each type of the controller, there are some derived sufficient conditions under which the whole closed loop fuzzy time-delay system is asymptotically stable. Moreover, those sufficient conditions can be transformed into the linear matrix inequality (LMI) problem. Then the controllers can be obtained by solving LMIs. Finally, a practical continuous stirred tank reactor (CSTR) system illustrates the control design and its stabilization effectiveness.