On the Laguerre Rational Approximation to Fractional Discrete Derivative and Integral Operators

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Abstract

This note ties the Laguerre continued fraction expansion of the Tustin fractional discrete-time operator to irreducible Jacobi tri-diagonal matrices. The aim is to prove that the Laguerre approximation to the Tustin fractional operator $s^{-nu}$ (or $s^{nu}$) is stable and minimum-phase for any value $0 < nu < 1$ of the fractional order $nu$. It is also shown that zeros and poles of the approximation are interlaced and lie in the unit circle of the complex $z$-plane, keeping a special symmetry on the real axis. The quality of the approximation is analyzed both in the frequency and time domain. Truncation error bounds of the approximants are given.

Autore Pugliese

Tutti gli autori

  • Maione G

Titolo volume/Rivista

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Anno di pubblicazione

2013

ISSN

0018-9286

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

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Non Disponibile

Numero di citazioni Scopus

18

Ultimo Aggiornamento Citazioni

2017-04-23 03:20:56

Settori ERC

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Codici ASJC

Non Disponibile