Research On Stability For The Uncertain Nonlinear Systems With Interval Time-varying Delay

In recent years, the problems of the stability of uncertain nonlinear time-delay systemhas always been a hot spot in the research of the control theory. Uncertainty, nonlinear andtime delay are common exist in the actual system. Delay tends to the performance of thesystem, so that its performance is poor, even lead to system instability, so the time delayof system has been more and more important for the scholars to research. Based on theanalyze, research absorbing for the existing achievements of domestic and foreign, paperresearches the stability and robust control problems about uncertain nonlinear system withinterval time-varying delay, from two different aspects discusses the stability of thesystem respectively, then obtains the more good conclusion.First of all,the basic knowledge about research was briefly introduced. Then a newLyapunov function was established about the single, double, triple and quadruple integralsfunctions, then using a single, double, triple integral inequalities, convex combinationhand with the derived functions, then the stability conditions for nonlinear system ofinterval time-varying delay was got, so the stability conditions for uncertain nonlinearsystem with interval time-varying delay was. At the end of research, the feasibility andefficiency of the conditions were verified by numerical simulation.The paper, further, the sufficient condition of the system which is uncertain nonlinearsystem withH parametric was obtained through introducing appropriate dimensionmatrixes.The paper finally discussed the problem of uncertain nonlinear system with intervaltime-varying delay from the terms of time-varying delay, this is the first time introducedthe delay variable for the problem about researching uncertain nonlinear system withinterval time-varying delay. This was used first time in the Lyapunov function, that is thetime-varying delay was introduced in the outer integral, so as to the dependence of thestability results is stronger. Using relevant lemmas, a sufficient condition of the stabilityfor nonlinear system with interval time-varying delays was obtained. so uncertainnonlinear system was. Compared the front Lyapunov function, this Lyapunov functionhave the stronger dependence. Applying this relevant lemmas, stability condition of lower conservative was finally got.