Approximate controllability of abstract stochastic impulsive systems with multiple time-varying delays

This paper investigates the approximate controllability of abstract stochastic impulsive systems with multiple time-varying delays. The class of stochastic impulsive systems consists of ordinary differential equations effected by impulse and noise environment. We focus first on constructing the control function. With this control function, we present sufficient conditions for approximate controllability problems in Hilbert space. The results are then extended to more easily verified conditions. The methods we choose are mainly Nussbaum fixed point theorem and stochastic analysis techniques combined with a strongly continuous semigroup. Finally, an example is given to illustrate the effectiveness of the results. Copyright (c) 2012 John Wiley & Sons, Ltd.