Analysis For Uncertain Systems With Time-delays

This paper considers the problems of stability analysis for uncertain systems with time-delays. Based on the theory of stability, by constructing a new Lyapunov-Krasovskii functional with using integral inequality and other mathematical skills, some new delay-dependent stability criterion are given. Among them, the main contents of the study include the following three parts:Part Ⅰ:Consider the stability analysis problem for a class of time-delay systems with time-varying delay in a given interval. A new type of augmented Lyapunov-Krasovskii functional which contains some triple integral terms is constructed. By combining integral inequality method and convex combi-nation method, an asymptotically stable criterion is obtained. Numerical examples verify this analysis method for improving the existing results.Part Ⅱ: Discuss the problem of the delay-dependent robust stability of neutral systems with mixed delays and time-varying structured uncertainty. The uncertainty has a linear fractional uncertainty structure, and is more general. Firstly, the stability of the nominal system is studied. By constructing a new type of Lyapunov-Krasovskii functional, a sufficient conditions which can be used to determine the stability of the system is given. Again, the result will be extended to the uncertain neutral systems. Finally, numerical simulation demonstrate the feasibility and validity of the results.Part Ⅲ:Focuse on the stability analysis problem for uncertain stochastic systems with time de-lays. a Lyapunov-Krasovskii functional is constructed with using a delay decomposition approach. Based on stochastic stability theory, combined with the integral inequality scaling and other tech-niques, a new delay-dependent asymptotically stable condition is derived. Finally, a numerical exam-ple illustrates the effectiveness of this approach.