GE-evolution operator method for controllability of time-varying stochastic descriptor systems in Hilbert spaces

Abstract

Abstract Exact (approximate) controllability and exact (approximate) observability of time-varying stochastic descriptor systems are discussed by GE-evolution operator, i.e., generalized evolution operator, which is a generalization of evolution operator, in the sense of mild solution in Hilbert spaces. Firstly, necessary and sufficient conditions for the exact (approximate) controllability to time-varying stochastic descriptor systems are given by GE-evolution operator in Hilbert spaces. Secondly, necessary and sufficient conditions for exact (approximate) observability to time-varying stochastic descriptor systems are given by GE-evolution operator in Hilbert spaces and the dual principle is proved to be true. Thirdly, two illustrative examples are given.