The ppth moment exponential ultimate boundedness of impulsive stochastic differential systems

In this paper, we investigate the global ppth moment exponential ultimate boundedness of impulsive stochastic differential systems. Using Lyapunov functions and algebraic inequality techniques, some sufficient conditions ensuring the global ppth moment exponential ultimate boundedness of the systems are obtained. It is shown that an unstable stochastic differential system can be successfully stabilized by impulses, even more, an unbounded stochastic differential system can be made into a bounded system under a proper impulsive control law. An example is also given to explain our results.