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

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  • Rafał Stanisławski
  • Krzysztof J. Latawiec

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.

Suggested Citation

  • Rafał Stanisławski & Krzysztof J. Latawiec, 2016. "Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-9, July.
    • Handle: RePEc:hin:jnddns:9590687
    DOI: 10.1155/2016/9590687
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