Controllability and observability of linear stochastic systems in Hilbert spaces

Abstract

The classical theory of controllability and observability for deterministic systems is extended to linear stochastic time-varying systems defined on infinite dimensional Hilbert spaces. Two types of stochastic controllability (observability) are studied: approximate and complete controllability (observability). Tests for complete and approximate controllability (observability) are proved, and the relation between the controllability (observability) of linear stochastic systems and the controllability (observability) of the corresponding deterministic systems is studied.