Interval Observer Design for Discrete-Time Uncertain Takagi–Sugeno Fuzzy Systems

This paper proposes a novel interval observer design method for discrete-time Takagi-Sugeno fuzzy systems with parametric uncertainty, disturbances, and measurement noise. We present a new structure of interval observer with more design parameters, which can be used to broaden the application scope of interval observer design. For improving the accuracy of interval estimation, an L_∞ norm-based approach is used in the design of interval observer to attenuate the effect of the unknown disturbances, noise, and parametric uncertainty. Furthermore, the design conditions are formulated into a set of linear matrix inequalities, which can be efficiently solved. Numerical simulations are given to illustrate the effectiveness of the proposed method.

I. Introduction

As an effective tool for approximating complex nonlinear systems, Takagi–Sugeno (T–S) fuzzy model [1] has been intensively studied in modeling and control of nonlinear systems [2]–[5]. Since the state variables of many practical systems are not fully measurable, observer-based method has been widely used for control design of T–S fuzzy systems [6]–[8]. Therefore, it is important to study observer design for T–S fuzzy systems [9]–[11]. Rotondo et al. [12] consider unknown input observer (UIO) design for discrete-time T–S fuzzy systems. However, the method of UIO can be implemented only when specific match conditions are satisfied. This restricts the application scope of UIO.