An elementary proof of Kharitonov's stability theorem with extensions

1 September 1989

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control

Vol. 34 (9) , 995-998
https://doi.org/10.1109/9.35816

Abstract

Gives an elementary proof of Kharitonov's theorem using simple complex plane geometry without invoking the Hermite-Bieler theorem. Kharitonov's theorem is a stability result for classes of polynomials defined by letting each coefficient vary independently in an arbitrary interval. The result states that the whole class is Hurwitz if and only if four special, well-defined polynomials are Hurwitz. The paper also gives elementary proofs of two previously known extensions: for polynomials of degree less than six, the requirement is reduced to fewer than four polynomials; and the theorem is generalized to polynomials with complex coefficients.<>

Keywords

This publication has 7 references indexed in Scilit:

An alternative proof of Kharitonov's theorem
IEEE Transactions on Automatic Control, 1989
Invariance of a strict Hurwitz property for uncertain polynomials with dependent coefficients
IEEE Transactions on Automatic Control, 1987
A simple general proof of Kharitonov's generalized stability criterion
IEEE Transactions on Circuits and Systems, 1987
On robust Hurwitz polynomials
IEEE Transactions on Automatic Control, 1987
A simple proof of Kharitonov's theorem
IEEE Transactions on Automatic Control, 1987
Some discrete-time counterparts to Kharitonov's stability criterion for uncertain systems
IEEE Transactions on Automatic Control, 1986
Invariance of the strict Hurwitz property for polynomials with perturbed coefficients
IEEE Transactions on Automatic Control, 1984