Delay-dependent fuzzy controller design for stabilization of nonlinear systems with multiple non-commensurate time delays

Abstract

In this paper, the T-S fuzzy model approach is extended to design fuzzy controllers for the stabilizability of nonlinear systems with multiple non-commensurate time delays. Three types of fuzzy controllers are state feedback, observer-based state feedback, and output feedback fuzzy controller with time delay information. Based on the concept of the parallel distributed compensation (PDC) and the delay-dependent Lyapunov functional approach, some control design methods are proposed to stabilize the whole fuzzy time-delay system asymptotically. These design approaches are all dependent on time delays. By Schur complement, these sufficient conditions can be easily transformed into the problem of LMI's. The practical example based on the CSTR (continuous stirred tank reactor) model is given to illustrate the control designs and their effectiveness.