Simple conditions based on generalisations of the Routh-Hurwitz and Mikhailov criteria that ensure the absence of polynomial roots in an RHP sector straddling the positive real semi-axis ( S-stability) are presented. In particular, it is shown that S-stability is ensured if the phase variation of a suitable power of the original n th-degree characteristic polynomial is equal to nπ/2, which implies that the zeros of the real and imaginary parts of this power must satisfy an interlacing property similar to the interlacing property satisfied by Hurwitz polynomials according to the classic Hermite-Biehler theorem. The condition can be checked by means of Sturm sequences. Examples show how the proposed methods operate.

On polynomial zero exclusion from an RHP sector

Daniele Casagrande;Umberto Viaro
2018-01-01

Abstract

Simple conditions based on generalisations of the Routh-Hurwitz and Mikhailov criteria that ensure the absence of polynomial roots in an RHP sector straddling the positive real semi-axis ( S-stability) are presented. In particular, it is shown that S-stability is ensured if the phase variation of a suitable power of the original n th-degree characteristic polynomial is equal to nπ/2, which implies that the zeros of the real and imaginary parts of this power must satisfy an interlacing property similar to the interlacing property satisfied by Hurwitz polynomials according to the classic Hermite-Biehler theorem. The condition can be checked by means of Sturm sequences. Examples show how the proposed methods operate.
File in questo prodotto:
File Dimensione Formato  
polynomial_zero_exclusion_C4L-A02-4014.pdf

non disponibili

Tipologia: Versione Editoriale (PDF)
Licenza: Non pubblico
Dimensione 751.9 kB
Formato Adobe PDF
751.9 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11390/1140519
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? 2
social impact