Stochastic observability and applications.

*(English)*Zbl 1060.93019Linear stochastic systems described by a state differential equation and an algebraic output equation are considered. The concept of stochastic observability is presented and discussed in detail. Next, using the theory of stochastic differential equations and deterministic algebraic methods, several conditions for stochastic observability are formulated and proved. The relation between stochastic observability and exponential stability in mean square sense are pointed out. The special case of stochastic observability for systems described by Itô differential equations is also considered. Finally, many applications of stochastic observability are discussed. Similar problems have been studied in the publication [T. Morozan, “Stochastic uniform observability and Riccati equations of stochastic control”, Rev. Roum. Math. Pures Appl. 38, No. 9, 771–781 (1993; Zbl 0810.93069)].

Reviewer: Jerzy Klamka (Gliwice)

##### MSC:

93B07 | Observability |

93E03 | Stochastic systems in control theory (general) |

93E15 | Stochastic stability in control theory |

93C05 | Linear systems in control theory |

60J75 | Jump processes (MSC2010) |

60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |