Stability Analysis And Observer Design For T-S Fuzzy Positive Systems

T-S fuzzy positive systems are a new branch in systems theory.The problem that the structure of nonlinear system is relatively complex and the results are not a lot has been solved by the T-S fuzzy model.The nonlinear system can be analysed by mature linear systems theory.The positive systems are a kind of special systems.Due to the negative state variables are not meaningful in many practical applications,positive systems have been of great interest to many fields.The state variables and outputs remain non-negative performance,which was required by the definition of the positive system.It implies that many results for general systems are not available for positive systems.A lot of novel results have been reported by using the non-negativity characteristic of systems.There are few results of the stability and no method of the observer design for T-S fuzzy positive system.Based on the previous results,this paper is concerned with the positivity determination,stability analysis and observer design for T-S fuzzy normal systems and singular systems respectively and some applied theoretical results are obtained.The main contributions of this paper are summarized as follows:(1)This paper introduces the model of systems,the examples of applications,the development of theories and the research status of singular systems,T-S fuzzy systems and positive systems simply.And some definitions and lemmas are recalled.(2)The theorems of T-S fuzzy general systems to determine if the systems are positive are given based on the existing conclusion.According to the positivity of the state variables,the theorems to determine if the system is stable are established,which is significantly less conservative than the existing theorems.Based on this,observer-based controller for the unstable singular T-S fuzzy positive system is designed.(3)There are few results of the stability and no method of the observer design for T-S fuzzy positive system.We promote the theories of T-S fuzzy general positive systems to the singular systems.The singular systems are decomposed into the combination of differential systems and algebraic systems by the restricted equivalent transformations.Then the positivity and the stability of the singular systems are determined and the observer-based state feedback controller is designed which makes the system to be stable and positive by the theories of the general positive systems.(4)Numerical examples are given to demonstrate the effectiveness and applicability of the obtained theoretical results.