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.