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On the observability and detectability of continuous-time Markov jump linear systems. (English) Zbl 1029.93007
The authors consider a class of linear stochastic uncertain systems with Markovian jump parameters described by \[ {dx(t)\over dt}=A\bigl(r (t)\bigr)x(t),\;x(0)=x_0,\;r(0)=r_0 \tag{1} \]
\[ y(t)=C\bigl( r(t)\bigr)x(t)\tag{2} \] where \(\{r(t),t\in [0,+\infty)\}\) is a homogeneous finite-state Markovian process with right continuous trajectories and taking values in a finite set \({\mathfrak I}=\{1,2, \dots,s\}\), \(x\in\mathbb{R}^n\) and \(y\in\mathbb{R}^q\) are state and output vectors, respectively. \(A(r(t))\) and \(C(r(t))\) are known real constant matrices of appropriate dimensions.
The authors introduce a new concept of \(W\)-detectability and the set of observability matrices \(O\) that is related to the concept of \(W\)-observability for system (1), (2). The obtained result provides a testable condition for \(W\)-detectability.

93B07 Observability
60J75 Jump processes (MSC2010)
93E03 Stochastic systems in control theory (general)
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