Stability Analysis And Controller Design For A Class Of Time-varying Delay Systems

Time-delay is a kind of phenomenon that often occurs in engineering systems,which is the cause of system-performance declines,the system shock and system instability.Therefore,the stability analysis and controller design for time-delay systems are the problems that must be studied in the control field,which have important theoretical and practical significance.As the rapid develop of modern industry and the increase of the system module,the process of control becomes more and more complicated,and its complexity is mainly manifested in: the uncertainty,the time variation,the extreme nonlinearity and diversity of the system structural parameters.All these factors put higher requirements for the research of control field,we must consider these factors when we analyzing control systems.At present,the research on time varying delay systems has achieved fruitful results,on the other hand,many aspects still need further studies,and a lot of problems need to be solved.In this paper,the stability analysis and controller design of a class of time-varying delay systems are studied by using the free weighting matrix method.And H_?analyze stability and controller design of nonlinear systems with time-varying delay are studied by using Takagi-Sugeno fuzzy model.The research direction of this paper can divide into the following several points:(1)By using the free weighting matrix method for stability analysis and controller design of a class of time-varying delay systems.First,based on the linear time varying delay system model,which takes into account the variation of the system delay,and the lower limit of the time delay,which may not start from zero.In the meanwhile,noticing the uncertainty of the system parameters,so that we construct a new Lyapunov-Krasovskii functional,and based on that,the system stability is analyzed.Finally,numerical examples and system state response curves are used to verify the effectiveness of the proposed method.(2)In the actual control systems,there are various kinds of disturbance phenomena,in this situation,whether the system work properly,and how the system resist these disturbance,these problems also are discussed in this paper.This paper has achieve a stability criterion,which satisfied the system robust H_?performance index,then based on the criterion,the design of the controller is carried out.Theeffectiveness of this controller design has been illustrated by comparing with the related references.(3)All of the previous studies are based on linear time varying delay systems.However,most of the control systems used around us have nonlinear characteristics,so we need to analyze the nonlinear systems.In this paper,the T-S fuzzy model is used to analyze the nonlinear system.An augmented Lyapunov-Krasovskii functional was built by using time delay information.Then by calculating derivation of the functional and doing reasonable treatment of the integral terms,the corresponding controller design scheme is given.