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- W2164764095 abstract "Abstract—In a recent paper, an asymptotic analysis was used to addressthe zero structure of discretized continuous-time systems expressed inthe Euler (or forward difference) operator. Unfortunately, the analysisis flawed, so that Theorem 1 is true as stated only when the continuous-time relative degree is equal to two. In this paper, we indicate how theanalysis may be rectified.Index Terms—Discrete-time systems, poles and zeros. I. I NTRODUCTION In a recent paper, 1 the zeros of discretized continuous-time systemsexpressed in terms of the Euler (or forward difference) operator are addressed. The key idea where the matrices is that by consideringthe sampling period as a perturbation parameter, the zero dynamicsof the resulting discrete-time system expressed in the delta operator(the time-domain equivalent of the Euler operator [1]) are singularlyperturbed, even though the matrices in the discrete-time state-spacemodel are regular perturbations of their continuous-time counterparts.Theorem 1 of the above-mentioned paper states that the singularlyperturbed zero dynamics leads to a separation of time scales inwhich the component of the zero dynamics associated with the fasttime scale corresponds to the zeros introduced by the samplingprocess, the so-called sampling zeros (or discretization zeros [2]).Furthermore, it is argued the sampling zeros of discrete-time modelsexpressed in the delta operator become infinite in the fast samplinglimit.Unfortunately, the analysis is flawed, with errors at several keypoints in the development. In particular, the asymptotic formula forthe location of the sampling zeros of delta operator-based discrete-time systems presented in Theorem 1 is consistent with the resultsof [3] and [1] only when the continuous-time relative degree equalstwo. In this paper, we show how the analysis may be rectified.Preliminaries: A function" @default.
- W2164764095 created "2016-06-24" @default.
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- W2164764095 date "1998-01-01" @default.
- W2164764095 modified "2023-10-10" @default.
- W2164764095 title "Comments on Zeros of discretized continuous systems expressed in the Euler operator: an asymptotic analysis" @default.
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