Stability Analysis Of Stochastic Differential Systems With Impulses

The stability of impulsive control system is an issue for discussion. With expanding application of control systems, and growing complexity of the objects, the uncertainty of the systems and the environment and the rigid control requirements, challenge us to be be faced with this age. But the uncertainty in the complex control systems is one of the most crucial factors. Many mathematical tools, introduced into control investigation practically, and fast development of computer technology, lay a solid foundation for meeting this challenge. In recent years, stochastic differential equations have attracted much attention because the problems are not only academically challenging, but also of practically important and have played an important role in many ways such as option pricing, forecast of the growth of population, etc. Sometimes impulsive control can be used to stabilize some stochastic systems. In this paper, we use comparison theory, Lyapunov functions, LMIs, and analysis methods to get some stability criteria of stochastic systems with impulses. Impulsive control is used in many stochastic systems (linear systems and non-linear ones), including the conditions that have impulses at finite times or with Markovian switching. Also some examples are given to establish the efficiency of conclusions, in order to make the theory practicalThis dissertation is divided into four parts. Chapter one is the exordium. In chapter two, some stability criteria of p-moment stability for stochastic differential equations with impulsive jump and Markovian switching are obtained by using Liapunov function method. In chapter three, we have got the result of robust H_∞filtering for stochastic systems with parameter uncertainty and impulse effects at defined time instants by using an LMIs approach. In chapter four, through obtaining equivalence between the solution of stochastic differential delay equations under impulsive control and the solution of stochastic differential delay equations without impulses, we have established some stability criteria for these systems.