论文标题
重新审视Yakubovich的S-液体：非欧盟规范的稳定性和合同性
The Yakubovich S-Lemma Revisited: Stability and Contractivity in Non-Euclidean Norms
论文作者
论文摘要
最初提出了著名的S-lemma，以确保在绝对稳定性问题中存在二次lyapunov功能。然而，二次lyapunov函数无非是状态空间上的平方欧几里得规范（即内部产物引起的规范）。关于平方非欧盟规范$ v（x）= \ | x \ |^2 $是否可以用作lyapunov在稳定性问题中的功能。本文提出了一种新颖的非物质S-胶原，该新型s-lemma构成了由加权$ \ ell_p $ norms定义的这种功能的建设性标准。我们的广义S-周期为LUR'E型系统带来了新的绝对稳定性和绝对合同性标准，包括例如，Aizerman和Kalman猜想的正面lur'e系统的新简单证明。
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 $V(x)=\|x\|^2$ 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 $\ell_p$ 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 systems.
