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A new formulation of the Liénard–Chipart stability criterion

Published online by Cambridge University Press:  24 October 2008

S. Barnett
S. Barnett
Affiliation:
School of Mathematics, University of Bradford, Yorkshire
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Abstract

The Liénard–Chipart criterion for determining whether all the zeros of a real nth degree polynomial a(λ) have negative real parts involves calculation of only about half the Hurwitz determinants, the order of the largest being n − 1. It is shown, by using the companion matrix of a polynomial formed from a(λ), that the required determinants are equal to minors of a matrix whose order is ½ n or ½(n−1) according as n is even or odd. In either case this matrix is very easy to obtain A simple application of the result provides a criterion for a(λ) to be stable and aperiodic.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 269 - 274
Copyright
Copyright © Cambridge Philosophical Society 1971

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References

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