Relaxed observer design of discrete-time T-S fuzzy systems via a novel multi-instant fuzzy observer

This paper is concerned with the design of observer for discrete-time Takagi-Sugeno fuzzy systems. Under the framework of multi-instant matrix, a novel fuzzy observer and a new Lyapunov function, which are parameter-dependent on m-steps normalized fuzzy weighting functions, are proposed for conceiving less conservative observer design conditions. In particular, some existing fuzzy Lyapunov functions and fuzzy observers are special cases of the new Lyapunov function and fuzzy observer, respectively. Furthermore, the obtained fuzzy observer design conditions are further relaxed by fully considering the algebraic properties of m-steps normalized fuzzy weighting functions. Finally, a numerical example is given to illustrate the effectiveness of the proposed results.