The Stability Analysis Of A Class Of Uncertain Time-delay System

In the real world,the control of complex systems is always accompanied withdelayinterference, therefore, the stability analysis of the control system under distanbance is ofgreat significance for scientific research and engineering application.So based on theLyapunov stability theory，the stability analysis of a class of uncertain time-delay system isstudied in this paper.First, as nolinear subsystem exists in the control system, the subsystem is split intoindependent sector of the system based on the Lurie control system, and it is studied as thefeed back part of the close-loop control system.Second, for the stability boundary of Lurie control system, a class ofLyapunov-Razumikhn function is built. Based on Lyapunov-Razumikhn function, two typeof Lyapunov-RazumikhnFormula form by different ways scaling are obtained, and thestability boundary of time-varying delay is stuied in this paper. Finally, the time delaystability boundary of the Lurie control system is discussed when the control changes fromtime-varying delay system to time-delay system.Third, for thestability analysis of Lurie control system satisfied H infinite performance,two kinds of Lyapunov-Krasovskii function are built. Based on Lyapunov-Krasovskiifunction, two type of Lyapunov-Krasovskii function by way of S-procedure are constructed.And the decision of the stability condition of time-varying delay system with controllersatisfied H infinite performance is given through the LMIs. And the decision condition oftime-delay system without controller is given as a contrast.Finally, base on theplatform of MATLAB, the stability conditions of time-varing delaysystem and time-delay system through constructing the Lyapunov-Razumikhn function andthe Lyapunov-Krasovskii function is proved effective through the simulation results.