Randomly Varying Delay Hybrid Robust Control Of Interval Systems

Robust stability and controllability of stochastic differential system is an important subject in the stability theory and the control theory. Markovian process is the most important stochastic process. On the other hand, time delay and system parameters uncertainty are commonly encountered in practice and are often the important sources of instability. Robust stability of stochastic varying delay uncertainty differential systems with Markovian switching and controllability of hybrid stochastic delay interval differential systems are discussed in this paper.This paper is divided into four chapters. We summery the development history of stability theory and practical meaning of studying this paper in the first chapter. In chapter two,we introduce some basic theory about stochastic analysis, stochastic integral, It o formula and It o theorem. In chapter three, we place great emphasis on robust stability of linear and semi-linear stochastic variable delay uncertainty differential systems with Markovian switching, then we present some useful corollaries and an example. In the forth chapter, we place great emphasis on that the linear and semi-linear hybrid stochastic delay interval differential systems with Markovian switching are almost surely asymptotically stable with a variety of feedback controller. Moreover, we use the method of Lyapunov functions and our stabilization criterions are described in terms of linear matrix inequalities.