Elsevier

Automatica

Volume 35, Issue 9, September 1999, Pages 1543-1548
Automatica

Brief Paper
A periodically time-varying minimal partial realization algorithm based on twisting

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Abstract

The 1975 paper of Meyer and Burrus gave necessary conditions on the coefficients of a periodically time-varying difference equation to generate a prespecified set of impulse responses. The main contribution of the present paper consists of an algorithm that constructs the coefficients of such a periodically time-varying realization of minimal lag. Thus the algorithm solves the minimal partial realization problem for the periodically time-varying (scalar) case. We use a general technique (“twisting”) for associating a time-invariant system with a periodically time-varying system in such a way that the time-step is preserved. The technique plays an essential role in the ideas underlying the algorithm.

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    Citation Excerpt :

    In this case, the periodic system can be given a state-space finite-dimensional realization, as shown in Colaneri and Longhi (1995). The problem of finding a minimal periodic realization in the form of difference equation is investigated in Bittanti, Bolzern and Guardabassi (1985) and Kuijper (1999). If the system is time invariant with transfer function G(σ), by letting T=1, it is easy to see that Gλ(σ,t)=G(λ), which is indeed the gain between the input and output “amplitudes” ū-ȳ.

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Supported by the Australian Research Council. This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor F. Blanchini under the direction of Editor R. Tempo.

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