The Time-delay Dependent Robust Stability And Stabilization Of Uncertain Time-delay Systems

Time delay exists widely in engineering practice.Time delay often causes instability of the system,even leads to the deterioration of the system performance,and it has brought great difficulties in the stability analysis and controller design of the system,so it is very important to consider the stability of time delay system.In recent years,many scholars have done a lot of research on time-delay problems,and a large number of scientific research achievements have also been developed.In the time delay description of uncertain systems,due to the large conservatism of the sufficient conditions for the stability of the linear uncertain time delay system,the research on the delay dependent stability is of great significance.Time delay is an essential characteristic of a system,and it can not be completely eliminated.With the development of productivity and the progress of science and more and more complex controlled objects,it is very difficult for us to get the exact mathematical model.The system model usually has uncertainty and becomes more complex and difficult to analyze and control the time delay system.Therefore,the hot and difficult points of the research have also become the analysis of the time-delay systems.Comprehensive problems.In this paper,the stability and stabilization of uncertain time-delay systems are studied with uncertain time-delay systems.By using the Lyapunov stability theory,the stability analysis and stabilization of uncertain time-delay systems are discussed by using the free weight matrix technology,using the Leibniz-Newton formula and using the LMI technology,thus the sufficient conditions for the stability of the system are obtained,and the numerical examples are used to verify and explain.Firstly,the stability of the system is studied and the stability of the delay dependent system is studied.The numerical examples are used to verify and illustrate.Secondly,according to the stability of the time-delay systems studied,on the basis of linear time-delay systems is the main scope,using the Lyapunov second method,get the condition of the stability of time-delay systems and interval uncertain time-delay discrete systems is calm conditions.Numerical examples are used to verify and illustrate.In this paper,the problem of H_?stochastic stability analysis for singular system with time-varying delay and Markovian jumping is addressed.By employing a new Lyapunov functional and free weighting matrix technique,new delay dependent criteria for the stochastic nonlinear delay hybrid singular system with time delay have been established in terms of LMI(linear matrix inequalities).The result which we developed can be checked numerically using the LMI toolbox.