Stability of a Set of Multivariate Complex Polynomials with Coefficients Varying in Diamond Domain

Y. Q. Shi; S. F. Zhou

doi:10.1109/81.168930

Stability of a Set of Multivariate Complex Polynomials with Coefficients Varying in Diamond Domain

Y. Q. Shi, S. F. Zhou

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Recently, attention has been focused on the (open left half plane) stability of a family of polynomials having complex coefficients with their real and imaginary parts each varying in a diamond. It has been concluded that the stability of a diamond family of polynomials is equivalent to the stability of the specific 16 edge polynomials of the diamond. In this paper, this result is extended to n-variate case. It is proved that the scattering Hurwitz property of the certain 16n diamond edge polynomials can guarantee the scattering Hurwitz property of the whole diamond family of n-variate complex polynomials.

Original language	English (US)
Pages (from-to)	683-688
Number of pages	6
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	39
Issue number	8
DOIs	https://doi.org/10.1109/81.168930
State	Published - Aug 1992

All Science Journal Classification (ASJC) codes

Electrical and Electronic Engineering

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10.1109/81.168930

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title = "Stability of a Set of Multivariate Complex Polynomials with Coefficients Varying in Diamond Domain",

abstract = "Recently, attention has been focused on the (open left half plane) stability of a family of polynomials having complex coefficients with their real and imaginary parts each varying in a diamond. It has been concluded that the stability of a diamond family of polynomials is equivalent to the stability of the specific 16 edge polynomials of the diamond. In this paper, this result is extended to n-variate case. It is proved that the scattering Hurwitz property of the certain 16n diamond edge polynomials can guarantee the scattering Hurwitz property of the whole diamond family of n-variate complex polynomials.",

author = "Shi, {Y. Q.} and Zhou, {S. F.}",

note = "Funding Information: Manuscript received October 4, 1991; revised May IS, 1992. This work was supported by the National Science Foundation under Grant ECS-8922695. This paper was recommended by Associatc Editor F. Y. Chang. The authors are with the Department of Electrical Engineering, Wright State University, Dayton, OH 45435. IEEE Log Number 9203653.",

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N2 - Recently, attention has been focused on the (open left half plane) stability of a family of polynomials having complex coefficients with their real and imaginary parts each varying in a diamond. It has been concluded that the stability of a diamond family of polynomials is equivalent to the stability of the specific 16 edge polynomials of the diamond. In this paper, this result is extended to n-variate case. It is proved that the scattering Hurwitz property of the certain 16n diamond edge polynomials can guarantee the scattering Hurwitz property of the whole diamond family of n-variate complex polynomials.

AB - Recently, attention has been focused on the (open left half plane) stability of a family of polynomials having complex coefficients with their real and imaginary parts each varying in a diamond. It has been concluded that the stability of a diamond family of polynomials is equivalent to the stability of the specific 16 edge polynomials of the diamond. In this paper, this result is extended to n-variate case. It is proved that the scattering Hurwitz property of the certain 16n diamond edge polynomials can guarantee the scattering Hurwitz property of the whole diamond family of n-variate complex polynomials.

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Stability of a Set of Multivariate Complex Polynomials with Coefficients Varying in Diamond Domain

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