Nonquadratic Lyapunov Functions for Nonlinear Takagi-Sugeno Discrete Time Uncertain Systems Analysis and Control

This paper deals with the analysis and design of the state feedback fuzzy controller for a class of discrete time Takagi -Sugeno (T-S) fuzzy uncertain systems. The adopted framework is based on the Lyapunov theory and uses the linear matrix inequality (LMI) formalism. The main goal is to reduce the conservatism of the stabilization conditions using some particular Lyapunov functions. Four nonquadratic Lyapunov Functions are used in this paper. These Lyapunov functions represent an extention from two Lyapunov functions existing in the literature. Their influence in the stabilization region (feasible area of stabilization) is shown through examples, the stabilization conditions of controller for discrete time T-S parametric uncertain systems is demonstrated with the variation of the lyapunov functions between (k, k+1) and (k, k+t) sample times. The controller gain can be obtained via solving several linear matrix inequalities (LMIs). Through the examples and simulations, we demonstrate their uses and their robustness. Comparative study verifies the effectiveness of the proposed methods. Keywords—Nonquadratic Lyapunov functions; Non-PDC; Linear Matrix Inequality; Parametric Uncertain Systems; TakagiSugeno