Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi–Sugeno fuzzy systems

This paper provides simple and effective linear matrix inequality (LMI) characterizations for the stability and stabilization conditions of discrete-time Takagi–Sugeno (T–S) fuzzy systems. To do this, more general classes of non-parallel distributed compensation (non-PDC) control laws and non-quadratic Lyapunov functions are presented. Unlike the conventional non-quadratic approaches using only current-time normalized fuzzy weighting functions, we consider not only the current-time fuzzy weighting functions but also the ll-step-past (l⩾0l⩾0) and one-step-ahead ones when constructing the control laws and Lyapunov functions. Consequently, by introducing additional decision variables, it can be shown that the proposed conditions include the existing ones found in the literature as particular cases. Examples are given to demonstrate the effectiveness of the approaches.