On the existence of a positive realization |
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Authors: | Lorenzo Farina |
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Affiliation: | Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Via Eudossiana 18, 00184 Roma, Italy |
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Abstract: | The positive realization problem for linear systems is to find conditions, for a given transfer function with nonnegative impulse response, to have a realization such that the resulting system is a positive system. Recently, it has been shown that, under a mild assumption on the long-term behaviour of the impulse response, this problem is related to the maximum modulus poles only. In this paper necessary and sufficient conditions for positive realizability of discrete-time systems are given. They show that also nondominant poles play a role in the most general case. Positive realizability conditions for the continuous-time case are also given. |
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Keywords: | Positive realization Positive systems Polyhedral cones Linear systems |
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