Fractional‐Order Discrete‐Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional‐Order LTI SISO Systems

Rafał Stanisławski and Krzysztof J. Latawiec

Discrete Dynamics in Nature and Society, 2016, vol. 2016, issue 1

Abstract: This paper presents new results on modeling and analysis of dynamics of fractional‐order discrete‐time linear time‐invariant single‐input single‐output (LTI SISO) systems by means of new, two‐layer, “fractional‐order discrete‐time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre‐based approximation layer for the Grünwald‐Letnikov difference. A new stability criterion for discrete‐time fractional‐order Laguerre‐based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.

Date: 2016
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https://doi.org/10.1155/2016/9590687

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnddns:v:2016:y:2016:i:1:n:9590687

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