Stochastic GE-evolution operator method for controllability of time varying stochastic implicit systems in Banach spaces

This paper discusses exact and approximate controllability and exact and approximate observability of time varying stochastic implicit systems by GE-evolution operator method in Banach spaces. Firstly, we discuss existence and uniqueness of the mild solution to time varying stochastic implicit systems by stochastic GE-evolution operator in Banach space. Secondly, we discuss conditions for exact and approximate controllability and exact and approximate observability of the systems considered in terms of stochastic GE-evolution operator and the dual principle. Finally, an illustrative example is given.