Vaidyanathan, P. P. (1988) A new breakthrough in linear-system theory: Kharitonov's result. In: Twenty-Second Asolimar Conference on Signals, Systems and Computers. Vol.2. Maple Press , San Jose, CA, pp. 1-14. ISBN 0929029151. http://resolver.caltech.edu/CaltechAUTHORS:20120621-104329715
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Abstract
Given a real coefficient polynomial D(s), there exist several procedures for testing whether it is strictly Hurwitz (i.e., whether it has all its zeros in the open left-half plane). If the coefficients of D(s) are uncertain and belong to a known interval, such testing becomes more complicated because there is an infinitely large family of polynomials to which D(s) now belongs. It was shown by Kharitonov that in this case it is necessary and sufficient to test only four polynomials in order to know whether every polynomial in the family is strictly Hurwitz. An interpretation of this result in terms of reactance functions (i.e., LC impedances) was recently proposed. These results were also extended recently for the testing of positive real property of rational transfer functions with uncertain denominators. In this paper we review these results along with detailed proofs and discuss extensions to the discrete-time case.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 1988 IEEE. Date of Current Version: 06 August 2002; Issue Date: 1988. Work supported in parts by the National Science Foundation grants DCI 8552579 and MIP 8604456. | |||||||||
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| Record Number: | CaltechAUTHORS:20120621-104329715 | |||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20120621-104329715 | |||||||||
| Official Citation: | Vaidyanathan, P.P.; , "A New Breakthrough In Linear-system Theory: Kharitonov's Result," Signals, Systems and Computers, 1988. Twenty-Second Asilomar Conference on , vol.1, no., pp.1-14, 1988 doi: 10.1109/ACSSC.1988.753943 Vaidyanathan, P.P.; , "A New Breakthrough In Linear-system Theory: Kharitonov's Result," Signals, Systems and Computers, 1988. Twenty-Second Asilomar Conference on , vol.1, no., pp.1-14, 1988 doi: 10.1109/ACSSC.1988.753943 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 32003 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Jason Perez | |||||||||
| Deposited On: | 21 Jun 2012 23:22 | |||||||||
| Last Modified: | 26 Dec 2012 15:21 |
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