Further studies on stability and stabilization conditions for discrete-time T-S systems with the order relation information of membership functions

This paper is concerned with the stability and stabilization problem for discrete-time Takagi-Sugeno (T-S) fuzzy systems. By taking into account the order relation information of membership functions (MFs), a so-called pseudo-MF vector is obtained through the transformation matrix; an improved approach to constructing the transformation matrix is given in order to make the best of the information of the MFs. Based on the transformed T-S fuzzy systems, relaxed stability and stabilization conditions are derived via both quadratic and non-quadratic Lyapunov functions. Numerical examples are provided to illustrate the effectiveness of the proposed approach.