Controllability of nonlinear stochastic neutral impulsive systems

The impulsive differential equations provide a natural description of observed evolutionary processes, which are subject to short term perturbations acting instantaneously in the form of impulses. Uncertainty can be incorporated either as an expression of our lack of precise knowledge or as a true driving force. In the latter case it is useful to model the system by a stochastic or noise driven model which leads to the study of stochastic impulsive differential systems. In this paper, the notion of complete controllability for nonlinear stochastic neutral impulsive systems in finite dimensional spaces is introduced. Sufficient conditions ensuring the complete controllability of the nonlinear stochastic impulsive system are established. The results are obtained by using the Banach fixed point theorem. Several forms of integrodifferential impulsive systems are indicated. Two examples are discussed to illustrate the efficiency of the obtained results.