1987•IEEE Transactions on Circuits and SystemsRequires access

A simple general proof of Kharitonov's generalized stability criterion

N.K. Bose, Y. Shi

Open publisher page 82 citations

Abstract

In a paper published in 1978 in Russian, Kharitonov proved that the strict Hurwitz property of a set of interval polynomials having complex coefficients may be established from the strict Hurwitz property of eight extreme polynomials. The proof of this significant result is advanced using elementary concepts in circuit theory. The approach not only provides a clear and complete proof of Kharitonov's generalized stability criterion but also has potentialities for generalization to the bivariate and, subsequently, the multivariate polynomial cases.

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What this paper is about

In a paper published in 1978 in Russian, Kharitonov proved that the strict Hurwitz property of a set of interval polynomials having complex coefficients may be established from the strict Hurwitz property of eight extreme polynomials. The proof of this significant result is advanced using elementary concepts in circuit theory. The approach not only provides a clear and complete proof of Kharitonov's generalized stability criterion but also has potentialities for generalization to the bivariate and, subsequently, the multivariate polynomial cases.

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OpenAlex reports 82 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In a paper published in 1978 in Russian, Kharitonov proved that the strict Hurwitz property of a set of interval polynomials having complex coefficients may be established from the strict Hurwitz property of eight extreme polynomials. The proof of this significant result is advanced using elementary concepts in circuit theory. The approach not only provides a clear and complete proof of Kharitonov's generalized stability criterion but also has potentialities for generalization to the bivariate and, subsequently, the multivariate polynomial cases.

Key concepts: Routh–Hurwitz stability criterion, Kharitonov's theorem, Generalization, Mathematics, Bivariate analysis, Stability (learning theory), Simple (philosophy), Applied mathematics

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