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IMA Journal of Mathematical Control and Information 2004 21(3):323-344; doi:10.1093/imamci/21.3.323
© 2004 by Institute of Mathematics and its Applications
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Stochastic observability and applications

Vasile Dragan1 and Toader Morozan1

1 Institute of Mathematics of the Romanian Academy, PO Box. 1-764, RO-70700, Bucharest, Romania

In this paper the problem of stochastic observability of a linear system affected by multiplicative white noise and Markovian jumping is investigated. The definition of stochastic observability adopted here extends to this framework the definition of the well known uniform observability of a deterministic time-varying linear system. By several examples we show that the concept of stochastic observability introduced in this paper is less restrictive than those introduced in other existing works and it does not always imply stochastic detectability as would be expected. Finally we prove that this kind of stochastic observability allows us to derive a Barbasin–Krasovskii type result for exponential stability in mean square. This provides a sufficient condition which guarantees that any semipositive solution of corresponding Riccati differential equation is a stabilizing solution.

Keywords: stochastic systems; stochastic observability; stochastic stability; Riccati differential equations.

Received 23 June 2003.


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