Research On Exponential Stability In Mean-square For Mixed Time-delay Systems With Convex Poiytopic Uncertainties

The research on theory of modern control systems occurs in automatic control,electronic technology, computer science and other subjects of mutual influence.These theories have been applied in the field of aerospace, and then applied inmany other areas widely. In recent years, with the advent of high-performancecomputers, modern control methods have been successfully applied in high-techfields of aerospace, power systems, industrial engineering and communicationsengineering. Especially, systems with convex polytopic uncertainties have receivedconsiderable attention of many scholars as an important research subject of moderncontrol theory. However, due to complexity of the systems, many scholars haveturned their attention to the stability of stochastic systems with Markovian jumpand convex polytopic uncertainties. All those Markovian jump systems can bedescribed as the hybrid systems with the time-evolving and event-drivenmechanism. In other words, these Markovian jump systems consist of a class ofsystems, which go on with time and their modes switch stochastically. Markovianjump systems with convex polytopic uncertainties always can exit in the randomcomponent failures and maintenance of interconnected subsystems, environmentchange suddenly.This dissertation investigates exponential stability in mean-square fortime-delay systems with polytopic uncertainties and Markovian jump.a) In order to guarantee the exponential stability for Markovian jump systemswith convex polytopic uncertainties and delay-dependent. Based on the methodof Lyapunov function and LMI, a sufficient condition is proposed forexponential stability in mean-square for Markovian jump systems with convexpolytopic uncertainties and delay-dependent.b) Considering varying delay and distributive delay, a sufficient condition ispresented to make a system with Markovian jump parameters and randomperturbation exponential stability using Lyapunov function and LMI.