Abstract
This paper discusses theH-index problem for stochastic linear discrete-time systems. A necessary and sufficient condition ofH-index is given for such systems in finite horizon. It is proved that when theH-index is greater than a given value, the feasibility ofH-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.
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