On the Stochastic Observability and Controllability

Abstract The notions of the stochastic observability and controllability are defined, and necessary and sufficient conditions for these properties to hold, are established. These properties reduce respectively to the complete observability and controllability when the original system degenerates to the deterministic one. If the statistical properties of the initial value are unknown, and moreover, if the covariance matrix of the measurement noise may be degenerate, explicit expression of the linear minimum covariance estimates for the states as well as for the initial value are also given in this paper.