In actual production and life,time-varying systems are in the leading position.As a kind of time varying system which the state space matrices with parameters variation,the linear parameter-varying(LPV)systems are more and more concerned.At the same time,time delays,which are common in the number of industrial processes,will be a main source of bad performance or even instability for control systems.Thus,it is noticed that the control problem of LPV systems with time delays becomes the focus of the control field.Therefore,this paper,by constructing proper Lyapunov function,systematically and deeply investigates the problems of affine quadratic stability and H∞ state feedback control for LPV systems with state delays in terms of parameterized linear matrix inequalities(PLMIs).For LPV system,this paper proposed a kind of design method of robust H∞variable gain controller,the method through LPV system of convex decomposition technology,will variable parameter systematic into LPV model which has structure of convex polyhedron.Next,the vertices of the convex polyhedron respectively design controller of meeting robust H∞ Performance indicators.So,we just to consider vertices of the convex polyhedron in designing LPV controller and analysis system stability,possessing more virtues that calculation volume small and more easily achieved.And in order to better guarantee the steady-state and dynamic performance,this section will closed loop pole assignment to the required area.Finally,variable gain controllers of Buck converter based on LPV model is designed,and simulation results demonstrate the feasibility of the method.This paper studies design problem of memory-less state feedback controller for time-delays affine LPV system.According to the quadratic definition of affine stability,the analysis and design conditions of the state feedback controller are derived by constructing the appropriate Lapunov function of the dependent parameters.Based on the multi convex method,the infinite dimensional problem is transformed into a finite dimensional problem.And because of the existence of coupling terms in solution conditions,by means of projection theorem and additional matrix,the non-LMIs is transformed into LMIs.Through numerical examples are given to validate the proposed theoretical feasibility.Next,based on the study of memory-less state feedback controller for time-delay affine LPV system,proposes memory state feedback controller research in a similar way.Through the MATLAB software simulation,compared with the memory-less state feedback controller,further verify the effectiveness of the memory state feedback controller. |