Research On Robust Stability And Control For A Class Of Uncertain Systems With Time-delay

In practical dynamic systems,time delays are general,which can be found in various engineering systems such as power systems,network communication systems,chemical processes and biological systems.Otherwise,in engineering practice,because of the precise model is difficult to establish or its too complex, we often simplified the model when analysis and design the system,and the influence of external disturbance, uncertainty is widespread on control system.The existence of uncertainty and time delay often lead to system analysis and synthesis becomes difficult, tend to be important factors lead to system instability, so it is necessary to do in-depth analysis of the stability of system and design a satisfactory controller.This article is mainly based on the robust H∞ control theory and lyapunov stability theory, important mathematical tools-linear matrix inequality(LMI),mainly discussed with norm bounded uncertain parameters of time-delay systems, the stability analysis and robust controller of the system.Through constructing suitable Lyapunov function,LMI approach and the method of integral inequality, corresponding to three different systems, three different control strategies are proposed.The detailed contents are as follow:(1) The problem of robust H∞ controller design for uncertain linear time invariant discrete system with control delay and external disturbance is studied.Based on Lyapunov stability theory, according to ordinary experience,constructing suitable Lyapunov function, through formula derivation calculus, in the form of linear matrix inequality(LMI) condition of asymptotic stability of the system is given and it is concluded that the robust H∞ control law and performance index g.Then discussed the H∞ optimal control problem and a method of optimal control parametric law has been designed.Finally,the example of actual networked control systems is given to illustrate that the analysis method and result are valid and feasible.(2) Then such a class of uncertain linear systems is studied, it also contains the control input delay and time-varying delayed state. By new type of quadratic integral inequality, it is on the basis of liberty matrix combining Park inequality, constructing Lyapunov function associated with upper and lower boundary information delay,to get delay-dependent conditions of a class autonomous systems and further design the robust H∞ control law. Finally, a numerical example is given to illustrate the better performance and less conservative.(3) Research about a class of uncertain time-delay system which system state variables are not easy to measure through the establishment of state observer and the use of LMI toolbox to solve linear inequality,designed the system robust controller under state observer,the last in this paper, the theorem is deduced with a numerical example to verify that the simulation results show when system parameters satisfy certain conditions, the theorem of this paper can guarantee the system robust H∞ asymptotically stable.