We study the identification problem for third-order linear time invariant positive systems in experiments where the output is a Poisson process. The problem well-posedness is investigated when the input-output model is described by a sum of real exponentials. A maximum likelihood procedure is then proposed and the admissible set for the unknown parameters is characterized. The novelty of the approach consists in solving a constrained maximum likelihood problem to estimate residues and eigenvalues based on theoretical results on minimality of positive realizations recently obtained in the literature. Numerical results are also provided. (C) 2002 Elsevier Science Ltd. All rights reserved.
Identification of positive linear systems with Poisson output transformation / DE SANTIS, Alberto; Farina, Lorenzo. - In: AUTOMATICA. - ISSN 0005-1098. - STAMPA. - 38:5(2002), pp. 861-868. [10.1016/s0005-1098(01)00277-1]
Identification of positive linear systems with Poisson output transformation
DE SANTIS, Alberto;FARINA, Lorenzo
2002
Abstract
We study the identification problem for third-order linear time invariant positive systems in experiments where the output is a Poisson process. The problem well-posedness is investigated when the input-output model is described by a sum of real exponentials. A maximum likelihood procedure is then proposed and the admissible set for the unknown parameters is characterized. The novelty of the approach consists in solving a constrained maximum likelihood problem to estimate residues and eigenvalues based on theoretical results on minimality of positive realizations recently obtained in the literature. Numerical results are also provided. (C) 2002 Elsevier Science Ltd. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
