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

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Abstract
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.