Robust Stability Of Uncertain Neutral Systems With Mixed Time-varying Delays

This paper studies the mixture of neutral systems with time-varying delays robust stabilization problem.Firstly,the Lyapunov function is structured,and the Newton-Leibniz formula and schur complement lemma,using the method of the free weighting matrix and linear matrix inequality is applied.Thus the sufficient condition is got which is relevant to the time delay dependent stability in the systems by applying the matlab simulink.This paper includes the following aspects:At first,the origin and the general situation of cybernetics are reviewed,and the background as well as the scientific research of time-delay systems and the robust systems are introduced.Secondly,the neutral systems with time-varying delays is given.And then an appropriate Lyapunov function should be selected,combining with the Newton-Leibniz formula method,introducing the free weighting matrix,and using Schur complement lemma and the feasible of linear matrix inequality.And a criterion for the robust stability of the system is got.This method has small amount of calculation.And finally,some numerical examples confirms that the proposed method is effective.Thirdly,on the basis of the last chapter,further research on that is done.The existing uncertainties is turned into the nonlinear term.Also,a new criterion by using the same method is got.Still,that the proposed method is effective through some numerical examples is proved.Finally,from the verification above,the article is summarized.