Two Plus Asymptotic Stability Analysis Of Time-delay Systems

In reality, the change trend of many systems is not only with the current state, but alsodepends on the state of the past. This phenomenon is called “time delay”. In recent years, thestability of time-delaying systems has become a hot problem, which attracts many scholars’attentions. And they have gained a lot of considerable progress. Because of the impact of thenetwork environment, the networked control system can be seen as the multiple time-varyingdelays system. To this kind of multiple time-varying delays system, this paper taking twoadditive delays for example studies asymptotically stability problems with certain parametersand get stability criterions. On this basis, we can extend our result to the time delay systems withnonlinear perturbation, and offer a stability criterion.My thesis is organized as follows:In the first chapter we briefly introduce the background of the networked control system, itsbasic problems and development. Then we build its model to multiple time-varying delayssystem. In the end, we put forward the research problem of this paper.In the second chapter we describe the preparative knowledge including Lyapunov stabilitytheory, LMI and several necessary lemmas, making full preparation for the next work.In the third chapter we analyze the asymptotic stability for network systems with twoadditive delays. Based Lyapunov stability theory and the linear matrix inequalities techniques,we construct an appropriate new Lyapunov-Krasovskii functional and deal with its derivativewith new inequality and convex polygon method. The delay-dependent stability criterion isconcluded. Finally, we obtain the numerical simulation results in LMI tool case of MATLAB andtestify the feasiblity of stability criterion.In the fourth chapter we extend the result in the third chapter to the time delay systems withtwo additive delay components with nonlinear perturbation. Based Lyapunov stability theory andthe linear matrix inequalities techniques, we construct an appropriate new Lyapunov-Krasovskiifunctional and deal with its derivative with S-procedure and convex polygon method. Thedelay-dependent stability criterion is concluded. Finally, we obtain the numerical simulationresults in LMI tool case of MATLAB and testify the feasiblity of stability criterion. In the fifth chapter we summarize the paper and proposes the problem for further research.