Controllability and Observability of Stochastic Singular Systems in Banach Spaces

Exact (approximate) controllability and exact (approximate) observability of stochastic singular systems in Banach spaces are discussed. Firstly, the condition for the existence and uniqueness of the mild solution to stochastic singular systems is given by GE-semigroup in Banach spaces. Secondly, the necessary and sufficient conditions for the exact (approximate) controllability and exact (approximate) observability of the systems considered are derived in terms of GE-semigroup, and the dual principle is given. Thirdly, an illustrative example is given.