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(J, J′)-Spectral factorization and conjugation for discrete-time descriptor system

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Abstract

This paper considers a (J, J′)-spectral factorization of a signed spectral matrix associated with a discrete-time improper transfer matrix by using the descriptor system representation and the generalized algebraic Riccati equation (GARE). Under the assumption that the improper transfer matrix is stable, a numerical algorithm for (J, J′)-spectral factorization is developed based on solutions of the generalized eigenvalue problem (GEP) and a related matrix equation. For an unstable transfer matrix, aJ-unitary conjugation method is applied to obtain a stable transfer matrix generating the same signed spectral matrix. Then a Hankel norm model reduction problem is briefly discussed. A simple example is also included to illustrate the numerical procedure.

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  1. Department of Applied Mathematics and Physics, Graduate School of Engineering, Kyoto University, 606-01, Kyoto, Japan

    Tohru Katayama

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  1. Tohru Katayama
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Katayama, T. (J, J′)-Spectral factorization and conjugation for discrete-time descriptor system. Circuits Systems and Signal Process 15, 649–669 (1996). https://doi.org/10.1007/BF01188987

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  • DOI: https://doi.org/10.1007/BF01188987

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