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1957•Transactions of the American Institute of Electrical Engineers Part I Communication and ElectronicsRequires access

A new application of the Hurwitz-Routh stability criteria

Theron Usher

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Abstract

WHEN THE HURWITZ-ROUTH stability criteria are applied to an algebraic polynomial with real coefficients, the existence, or nonexistence, of unstable roots of the polynomial is revealed. However, if the polynomial contains all stable roots, the criteria do not give an indication of the relative stability of the roots. The latter information is frequently desired.

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What this paper is about

WHEN THE HURWITZ-ROUTH stability criteria are applied to an algebraic polynomial with real coefficients, the existence, or nonexistence, of unstable roots of the polynomial is revealed. However, if the polynomial contains all stable roots, the criteria do not give an indication of the relative stability of the roots. The latter information is frequently desired.

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Available abstract

WHEN THE HURWITZ-ROUTH stability criteria are applied to an algebraic polynomial with real coefficients, the existence, or nonexistence, of unstable roots of the polynomial is revealed. However, if the polynomial contains all stable roots, the criteria do not give an indication of the relative stability of the roots. The latter information is frequently desired.

Key concepts: Routh–Hurwitz stability criterion, Hurwitz polynomial, Kharitonov's theorem, Stability (learning theory), Mathematics, Polynomial, Algebraic number, Control theory (sociology)

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