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This paper addresses positive observer design problem for discrete-time positive systems with multidelays. Both the positive observer and the positive systems share the nonnegativity of their states. The observer is of Luenberguer-type, which is an extension of the classical linear observer. A set of equivalent necessary and sufficient conditions is proposed for the existence of the Luenberguer-type positive observer. All the results are formulated as linear programming (LP) and linear matrix inequality (LMI) problems and therefore can be easily verified or implemented. The obtained theoretical results are demonstrated by a numerical example.

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