Stochastic observability and applications. (English) Zbl 1060.93019

Dragan, Vasile; Morozan, Toader

IMA J. Math. Control Inf. 21, No. 3, 323-344 (2004).

Linear 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)

Keywords:

stochastic observability; linear systems; stochastic systems; Markovian jump; multiplicative noise; exponential stability; Itô differential equations