Analysis of Fractional Order Polynomials Using Hermite-Biehler Theorem

ŞENOL B., YEROĞLU C., TAN N.

International Conference on Fractional Differentiation and its Applications (ICFDA), Catania, İtalya, 23 - 25 Haziran 2014 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası:
  • Doi Numarası: 10.1109/icfda.2014.6967425
  • Basıldığı Şehir: Catania
  • Basıldığı Ülke: İtalya
  • Anahtar Kelimeler: fractional order polynomials, stability, hermite-biehler theorem, interlacing property, SYSTEMS
  • İnönü Üniversitesi Adresli: Evet

Özet

This paper presents some results for stability analysis of fractional order polynomials using the Hermite-Biehler theorem. The possibilities of the extension of the Hermite-Biehler theorem to fractional order polynomials is investigated and it is observed that the Hermite-Biehler theorem can be an effective tool for the stability analysis of fractional order polynomials. Variable changing has been applied to the fractional order polynomial to transform it into an integer order one. Roots of this polynomial are found and verified with the roots obtained using the Hermite-Biehler theorem. Stability analysis has been done investigating the interlacing property of the polynomial. Results are verified with the Radwan procedure. The method is clarified via illustrative examples.