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Necessity in quadratic criterion for absolute stability
Author(s) -
Yakubovich V. A.
Publication year - 2000
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/1099-1239(200009/10)10:11/12<889::aid-rnc531>3.0.co;2-x
Subject(s) - quadratic equation , mathematics , stability (learning theory) , absolute (philosophy) , circle criterion , stability criterion , quadratic form (statistics) , computer science , exponential stability , nonlinear system , statistics , philosophy , geometry , epistemology , machine learning , physics , discrete time and continuous time , quantum mechanics
In the main part of this paper we consider the linear system together with some integral quadratic constraints. It is known that many nonlinearities encountered in practice satisfy such constraints. The criterion for absolute stability of this system is formulated and proved. The slightly different quadratic criterion was proved by the author earlier as sufficient condition for absolute stability. We prove that the criterion formulated here is not only sufficient but also necessary for absolute stability. The new proof of sufficiency is also presented. Some generalizations of this result and several examples of applications of the quadratic criterion are given. Copyright © 2000 John Wiley & Sons, Ltd.