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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Imprimer: 1064-2315
ISSN En ligne: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v43.i8.10
pages 1-18

Identification Problems of Linear Stationary Systems. Part I. Prony's Method

Vladimir B. Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Alexander S. Apostolyuk
National Technical University of Ukraine "Kiev Polytechnical Institute", Kiev, Ukraine

RÉSUMÉ

The survey of algorithms of solving of one of the simplest identification problems, which however has numerous applications, namely, the problem of determination of parameters of linear stationary system with continuous time by results of registration in discrete instants of time of transient process in this system is presented. We assume that the order of the system is known. Registration error is modeled by means of account of only fixed number of significant digits after decimal point. The considered algorithms are based on the idea of the Prony’s method about decomposition of the general identification problem to the problem of determination of exponent powers and subsequent finding of amplitudes of the corresponding modes. We note that according to the Prony’s method and the method of matrix pencils decomposition is realized by means of transition from the system with continuous time to the corresponding system with discrete time. Subsequent (inversed) transition from the system with discrete time to the system with continuous one in its turn can cause the additional errors of parameters estimates of initial system with continuous time.


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