版权所有:内蒙古大学图书馆 技术提供:维普资讯• 智图
内蒙古自治区呼和浩特市赛罕区大学西街235号 邮编: 010021
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:
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.