Output Feedback Control Of Continuous Time T-S Fuzzy Systems

Most of the actual systems are nonlinear systems,thus how to handle nonlinear systems has always been a hot spot for exploration.With the advancement of fuzzy theory,the use of fuzzy control theory to deal with nonlinear systems is favored by many scholars.For example,the T-S fuzzy model can approximate a smooth and bounded nonlinear function with arbitrary precision,and the nonlinear system is described as a convex combination of a set of local linear models.In-depth research has been conducted on the control synthesis of fuzzy systems and important results have been achieved,such as controller design,control etc.Mostly focused on state feedback.However,some states in the actual system are difficult to measure or the measurement cost is very high.Therefore,it is meaningful to study the output feedback control of the T-S fuzzy systems.This paper mainly improves and expands the shortcomings in the output feedback control of the continuous-time T-S fuzzy systems.The main work is as follows:(1)The output feedback H_? control of the systems is explored,and the design methods of static and dynamic output feedback controller are given.First,the nonquadratic Lyapunov function and the non-parallel distributed compensation controller are designed,and a new method is given to bound time-derivatives of the membership functions.Secondly,using the equivalent lemma and inequality scaling,the sufficient conditions for the static output feedback controller and the dynamic output feedback controller to stabilize the closed-loop system are obtained,respectively.And the Lagrange multiplier method is used to solve the system's attraction domain,which reduces the computational complexity due to search parameters.(2)The dynamic output feedback H_? control of the systems is studied,and a simple and effective design method of dynamic output H_? controller is given.First,a Lyapunov function without special structure is designed,and the inequality condition that restricts the time derivative of the membership functions are given.Secondly,using the equivalence lemma and the characteristics of the membership functions,the stable condition with less conservativeness is obtained and the H_? performance is satisfied.In addition,the relaxation technique proposed in this paper is also suitable for fuzzy systems with unmeasurable premise variables.(3)The control synthesis of nonlinear systems based on T-S model is studied.The more general conditions for the existence of state feedback and static output feedback controllers that satisfy the H_? performance in the Lyapunov level subset are respectively given.First,the idea of polynomial is used,and the extended non-quadratic Lyapunov functions and homogeneous polynomial non-parallel control laws are designed,and the inequality conditions for bounding the time derivative of the membership functions are given.Secondly,using the equivalent expansion lemma and the method of introducing slack variables,the sufficient conditions for the systems to be gradually stable under the H_? performance index are gained.In addition,the polynomial technology is extended to the design of dynamic output feedback controllers,and the conditions are less conservative.Finally,it is verified that as the degree of the polynomial increases,the H_? performance index gradually decreases.