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New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators

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  • Rafał Stanisławski
  • Marek Rydel
  • Krzysztof J. Latawiec

Abstract

This paper provides new results on a stable discretization of commensurate fractional-order continuous-time LTI systems using the Al-Alaoui and Tustin discretization methods. New, graphical, and analytical stability/instability conditions are given for discrete-time systems obtained by means of the Al-Alaoui discretization scheme. On this basis, an analytically driven stability condition for discrete-time systems using the Tustin-based approach is presented. Finally, the stability of discrete-time systems obtained by finite-length approximation of the Al-Alaoui and Tustin operators are discussed. Simulation experiments confirm the effectiveness of the introduced stability tests.

Suggested Citation

  • Rafał Stanisławski & Marek Rydel & Krzysztof J. Latawiec, 2018. "New Stability Tests for Discretized Fractional-Order Systems Using the Al-Alaoui and Tustin Operators," Complexity, Hindawi, vol. 2018, pages 1-9, November.
    • Handle: RePEc:hin:complx:2036809
    DOI: 10.1155/2018/2036809
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