Delay Dependent Stability Analysis Of Time Delay Systems

There often exist time-delay phenomena in practical control systems,which always results in poor performance of control systems,and the existence of time-delay often regarded as the main cause that leads to instability.Therefore,how to put the bad effects to eliminate or reduce to a minimum degree has been a research focus in the field of control engineering.In this paper,the stabiliy of two typical time-delay systems are studied.Based on the lyapunov stability theorem,we obtain delay-dependent stability criterion in terms of a linear matrix inequality by constructing proper LKF and using the methods of integral inequalities and other methods in the process of research.The main arrangement of the thesis are as follows:Stability of linear singular system with time-delay is studied.Firstly,we trans-form the linear singular time-delay system into a neutral system with a linear con-straint.Secondly,by using the new type of Wirtinger integral inequalities and the LKF method,we obtain a new delay-dependent stability criterion in terms of a lin-ear matrix inequality.Finally,a numerical examples show the new result that is less conservativeness than the before.Stability of linear system with time-varying delay is studied.We discuss the ef-fects of different integral inequalities on system stability and get the extended Jensen inequalities to deal with the derivative terms.we obtain a new delay-dependent stability criterion in terms of a linear matrix inequality by constructing the new lya-punov function and applying lyapunov stability theorem.A new less conservative criterion is given,and examples are used to demonstrate the method is effective.Finally,we summarize this thesis and look forward to the future,the further research on the stability of time-delay system is needed.