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arXiv

THE YAKUBOVICH S-LEMMA REVISITED: STABILITY AND CONTRACTIVITY IN NON-EUCLIDEAN NORMS

作     者:Proskurnikov, Anton V. Davydov, Alexander Bullo, Francesco 

作者机构:Department of Electronics and Telecommunications Politecnico di Torino Turin Italy Department of Mechanical Engineering The Center for Control Dynamical Systems and Computation University of California Santa Barbara United States 

出 版 物:《arXiv》 (arXiv)

年 卷 期:2022年

核心收录:

主  题:Lyapunov functions 

摘      要:The celebrated S-Lemma was originally proposed to ensure the existence of a quadratic Lyapunov function in the Lur e problem of absolute stability. A quadratic Lyapunov function is, however, nothing else than a squared Euclidean norm on the state space (that is, a norm induced by an inner product). A natural question arises as to whether squared non-Euclidean norms V (x) = ǁxǁ2 may serve as Lyapunov functions in stability problems. This paper presents a novel non-polynomial S-Lemma that leads to constructive criteria for the existence of such functions defined by weighted p norms. Our generalized S-Lemma leads to new absolute stability and absolute contractivity criteria for Lur e-type systems, including, for example, a new simple proof of the Aizerman and Kalman conjectures for positive Lur e *** Codes 34H05, 93C15 Copyright © 2022, The Authors. All rights reserved.

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