Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T16:36:35.903Z Has data issue: false hasContentIssue false
  • English
  • Français

Inclusion conditions for Hurwitzian and Schur sets in

Published online by Cambridge University Press:  24 October 2008

Russell A. Smith
Russell A. Smith
Affiliation:
University of Durham
Get access Rights & Permissions [Opens in a new window]

Abstract

A condition of frequency domain type on the vector polynomial G(z) is obtained which is both necessary and sufficient for the Hurwitzian set of G(z) to include the special Hurwitzian set , where E(z) = col (1, z, …, zn). This result is extended to Hurwitzian sets arising from scalar delay-differential equations. Analogous conditions are also given for each of the inclusions where denotes the Schur set of G(z).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 1 , July 1976 , pp. 113 - 120
Copyright
Copyright © Cambridge Philosophical Society 1976

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Marden, M.Geometry of polynomials, 2nd ed. (American Math. Soc., Providence R.I., 1966).Google Scholar
(2)Smith, R. A.Absolute stability of certain differential equations. J. London Math. Soc. (2) 7 (1973), 203–210.CrossRefGoogle Scholar
(3)Smith, R. A.On the elliptic ball stability criterion for ordinary differential equations. Proc. Cambridge Philos. Soc. 74 (1973), 497–505.CrossRefGoogle Scholar
(4)Smith, R. A.Elliptic ball stability criterion for discrete-time systems. Internat. J. Control 19 (1974), 925–932.CrossRefGoogle Scholar
(5)Smith, R. A.Absolute stability of feedback control equation with constant time lags. J. London Math. Soc. (2) 9 (1974), 346–354.CrossRefGoogle Scholar
(6)Szegö, G.Bemerkungen zu eine Satz von J. H. Grace über die Wurzeln algebraischer Gleichungen. Math. Z. 13 (1922), 28–55.CrossRefGoogle Scholar