The Study Of Stability And Sliding Mode Control Of A Class Of Impulsive Systems With State Time-delay

Impulse phenomenon is a very common object in our daily life, such as the heartbeat and blood circulation in the organism, the influence of abrupt climate changes topopulation growth as diverse as the impact of unexpected social events to the stock orthe financial market fluctuation and the shock of economic environment’s mutation onthe commodity supply and demand.The impulsive differential system is the most appropriate description of theimpulse phenomenon, which has been applied in many fields. And it draws a lotattentions and interests of many scholars all over the world due to its profoundpractical significance and application value in the research of many practicalproblems in various areas of science and technology. It has been gradually formed ahot spot in dynamic research.What the scholars most concern about is the influences of the impulse to the stateof systems. And the scholars are trying to reveal the essence change of the systemsbecause of the impulse phenomenon’s appearance. In the past study, it is found thatthe impulsive system is not simple sum of continuous system and discrete system, butsynthesizes the characteristics of the two kind systems and is beyond the scope ofcontinuous and discrete systems. There still are many fundamental problems to besolved as well as new study methods to be sought. Therefore the theoreticinvestigation of impulsive systems is full of attractive and challenging saying nothingof its theoretical significance.In recent years, it has obtained a lot of results in the research of impulsivesystems’ solution basic theory, boundary value problems and stability theory.However, the related research of impulsive systems with time-delay has rarely beenstudied. The difficulty of the research is brought about by the impulse phenomenonand the time delay together. The research of impulsive systems with time-delay is in its infancy, and temporary studies have focused on the stability of the system. There isfew results of the system stabilization control.In this thesis, a class of impulsive systems with time-delay has been studied onthe basis of past research.First, a brief introduction of the existence of impulse phenomenon and impulsivesystems research’s origin, history and current situation is given. And a generalintroduction of sliding mode control method which is used in this thesis is alsorecommended.In the second part, some new asymptotic stability condition of impulsive systemswithout state time-delay is obtained by using Lyapunov direct method and someinequations. Then the method is applied to a class of impulsive systems withtime-delay.In the third chapter, the study situation of impulsive system stabilization controlis introduced. Then using the sliding mode control method, two classes of systems aredesigned: one is with the time-delay in both state and control variable; another one iswith the time-delay only in state variable. Ultimately, a numerical example is given totest the reliability of the stability conditions.Finally, a conclusion is given as well as some further problems and aspects ofdirection of further research.