Stability Varying Delay Systems With Nonlinear Perturbation Additive

As is known to us, time-delay occurs in many practical engineering systems widely, andit is a major cause of instability, oscillation, and poor performance. In the past few decades,the stability of delay systems has attracted many scholars’ attention. It is easy to see a lotof important research results have been proposed in kinds of journals. However, a signalmay experiences a few segments of networks when it transmits from one point to another.So delays tend to have diferent characteristics in diferent actual systems, which leads tomultiple additive delays. The foregoing analysis shows that studying the stability analysisand control synthesis problem for systems with multiple additive time-varying delays is ofgreat signifcance not only in practice aspect but also in development trend.By taking two additive delays for example, this paper studies stability problems forinterval time-varying delay systems, and derive asymptotic stability criterion. On this basis,this paper researches the controller design problem for the system. We can extend our resultsto the time delay systems with nonlinear perturbations, and ofer a stability criterion.This thesis is divided into fve chapters:In chapter1, we introduce the background of the research for delay systems, and makea detailed review. On this basis, we indicate the main issues in this paper.In chapter2, In this chapter, we briefy introduce the theoretical knowledge of stability,like Lyapunov stability criterion and several important lemmas, which make full preparationfor the follow-up work.In chapter3, In this part, we discuss stability problems for interval delay systems withtwo additive time-varying delays components considering the situation of certain parameters.By constructing a proper Lyapunov-Krasovskii functional and according to use Jensen’sInequality and Reciprocally convex combination, we derive a new delay-dependent stabilitycriterion, which is based on Lyapunov stability theory and LMI techniques. Finally, we showthe result we obtained through the theoretical analysis and numerical example, which isbetter than some results have obtained at present already in conservatism and complexity.In chapter4, based on the results of the chapter3, we extend the results to time-delaysystems with two additive delay components considering the situation of certain parametersand with nonlinear perturbations. In the end, we show the feasibility of the obtained resultthrough a numerical example. In chapter5, we summarize the entire thesis, and point out the future researching di-rection.