Fuzzy Dynamic Output Feedback Controller for a Class of Discrete- Time Takagi -Sugeno Implicit Models with Unmeasurable Premise Variables

Abstract

This paper discusses the design problem of a fuzzy dynamic output feedback controller (FDOFC) for a class of discrete-time nonlinear implicit models described by Takagi-Sugeno (T-S) fuzzy structure with unmeasurable premise variables. The approach is based on the singular value decomposition. More precisely, using the fuzzy T-S observer in explicit structure and the Parallel Distributed Compensator (PDC) control law, a new result to investigate the FDOFC problem for the considered class of discrete-time T-S implicit models (DTSIMs) is then proposed. The guarantee of the global asymptotic stability of the closed-loop augmented system is proved by using the Lyapunov theory and the conditions of asymptotic stability are given in terms of linear matrix inequalities (LMIs). Finally, an application based on rolling disc process is presented as an illustrative example to show the performance of the proposed dynamic controller design.