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

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.