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IMA Journal of Mathematical Control and Information Advance Access originally published online on November 11, 2005
IMA Journal of Mathematical Control and Information 2006 23(3):371-394; doi:10.1093/imamci/dni064
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Observability and detectability of a class of discrete-time stochastic linear systems

Vasile Dragan** and Toader Morozan

Institute of Mathematics of the Romanian Academy, PO Box 1-764, RO-014700 Bucharest, Romania

** Email: vdragan{at}fx.ro

In this paper, the problem of stochastic observability and stochastic detectability of a class of discrete-time linear systems affected by independent random perturbations and Markovian jumping is investigated. The definition of stochastic observability adopted here extends to this framework the definition of the wellknown uniform observability of a deterministic discrete-time 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 imply always the stochastic detectability as it would be expected. Finally, one proves that this kind of stochastic observability allows us to derive a Barbashin–Krasovskii-type result for exponential stability in mean square.

Keywords: discrete-time stochastic systems; stochastic observability; stochastic detectability; stochastic stability.

Received on 3 November 2004. accepted on 11 July 2005.


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