Discussions on observer design of nonlinear positive systems via T-S fuzzy modeling

Xudong Zhao, Tingting Wu, Xiaolong Zheng, Ren Li

Abstract: In this paper, the problems of state estimation for nonlinear positive systems based on T–S fuzzy modeling will be investigated. It will be shown that some new issues naturally arise when designing observers for positive nonlinear systems by using T–S fuzzy modeling approach. The results are developed in the following two cases: first, for systems that can be modeled by T–S fuzzy model composed of all positive local subsystems, a novel quadratic Lyapunov function is proposed to reduce the conservativeness by some other existing methods; second, for derived T–S fuzzy model comprising non-positive subsystems, the observer design is converted into the problem of stability for a positive linear system, upon which, a new algebraic algorithm for constructing a observer is given. Two numerical examples are given to demonstrate the effectiveness and applicability of the obtained theoretical results.