Controller Design And Analysis Of Polynomial Fuzzy Switched Positive System Dependent On Membership Function

Nonlinear switched positive systems with time delay have important theoretical significance and extensive application background.The switching characteristics,non-negative system state variables,and inherent delays make the dynamic behaviour of the nonlinear switched positive system with time delay very complex.Stability analysis and control research for this system are essential and fundamental issues.This thesis takes nonlinear switched positive systems with time delay systems as the research object and the polynomial fuzzy model and interval type-2 polynomial fuzzy model are carried out to express this particular system.The exponential stability and positive analysis of continuous and discrete nonlinear switched positive systems with time delay are investigated based on the mode-dependent dwell time(MDADT)theory.Meanwhile,a new method to reduce the lower bound on MDADT is proposed,and the switched polynomial fuzzy controller is designed with imperfectly matched premises(IPC)technology.The main research contents of this thesis are as follows:(1)Exponential stability and positivity analysis for continuous-time nonlinear switched positive systems with time delay.For the model structure,with respect to the advantages of the polynomial fuzzy model,the polynomial fuzzy model is adopted to represent the dynamic characteristics of nonlinear switched positive systems with time delay,which can fully improve the approximation ability of the model.For the controller design,matrix decomposition is introduced to overcome the obstacle caused by the non-convexity conditions both in positive and stable conditions can not be solved by SOSTOOLs.In addition,the switched polynomial fuzzy controller is designed based on the IPC technology,which enhances the design flexibility and reduces the implementation cost.For the stability analysis,as the existing switching control theory is relatively conservative which leads to high bound of dwell time,a switched fuzzy copositive Lyapunov-Krasovskii function(SFCLKF)with upper bound of the derivative of the membership function and a Taylor expansion technique are together incorporated in positive switched stability analysis to obtain tight bound of dwell time and relax conditions.At last,a numerical example is provided to validate the proposed method.(2)Exponential stability and positivity analysis for discrete-time nonlinear switched positive systems with time delay.For the model structure,in view of the uncertainty of system parameters,the interval type-2 polynomial fuzzy model is used to model the nonlinear switched positive systems with time delay,in which the uncertainty of the system is fully represented in the interval type-2 membership function.For the controller design,the switched polynomial fuzzy controller is designed based on the IPC technology.To transform the non-convex stability condition into the convex condition,the polynomial fuzzy controller gain incorporates the Lyapunov function variables.For the stability analysis,the interval type-2 membership function dependent method prosed to relax the resulting conservative caused by the lack of membership functions.Finally,a numerical simulation proves the effectiveness of the proposed method in reducing the lower bound on MDADT.