Stability Study Of Time-delay Systems Based On Integral Inequality

Time delay exists in a variety of practical systems such as networked systems,chemical systems,and economic systems.In practical engineering applications,time delays are not only the reason of instability and poor control performance,but also may improve the controlling effect in some control systems.So,studies on the stability and control for time-delay systems have important theoretical and practical values.Firstly,in this thesis,the main methods used to deal with delay-dependent stability problems are summarized,especially,those involving the integral inequality approaches.Then,this thesis presents a refined integral inequality approach method,called the improved double integral inequality approach.Moreover,a new finite-sum inequality is proposed which is an improvement on the Abel lemma-based finite-sum inequality.Those present inequalities include more integral terms containing time-delay information.In particular,many literatures compare integral inequality approaches with free-weighting-matrix methods,and these two types of methods usually have their particular advantages while some integral inequality methods not only possess simple form and less decision matrix variables but also decrease the computational burden.So,our integral inequality method focuses on these merits.Secondly,by using the two inequalities and constructing appropriate Lyapunov-Krasovskii functionals(LKFs),this thesis investigates the delay-dependent stability of systems,including four types of time-delay systems: systems with a distributed delay;linear neutral systems;linear singular systems;and linear discrete time-delay systems.Delay-dependent stability criteria are obtained in terms of linear matrix inequalities(LMIs),and numerical examples demonstrate that these results are less conservative.Finally,the conclusion of research is summarized,and the future work is pointed out.