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\(\mathcal{H}_-\) index for stochastic linear discrete-time systems. (English) Zbl 1418.39003

Summary: This paper discusses the \(\mathcal{H}_-\) index problem for stochastic linear discrete-time systems. A necessary and sufficient condition of \(\mathcal{H}_-\) index is given for such systems in finite horizon. It is proved that when the \(\mathcal{H}_-\) index is greater than a given value, the feasibility of \(\mathcal{H}_-\) index is equivalent to the solvability of a constrained difference equation. The above result can be applied to the fault detection observer design. Finally, some examples are presented to illustrate the proposed theoretical results.

MSC:

39A12 Discrete version of topics in analysis
93B36 \(H^\infty\)-control
93B35 Sensitivity (robustness)
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