Separable Lyapunov functions for monotone systems: constructions and limitations
type: Item
instance of: scholarly article
title: Separable Lyapunov functions for monotone systems: constructions and limitations
zbMATH Open document ID: 1338.34102
author: G. Dirr
author: Hiroshi Ito
author: Anders Rantzer
author: Björn S. Rüffer
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2016-03-10T00:00:00Z
review text: The authors investigate the existence and construction of two types of Lyapunov functions for monotone dynamical systems defined on \(\mathbb{R}^n_+\) via the differential equation \(\dot{x} = f(x)\): sum-separable and max-separable Lyapunov functions. It is shown that both max-separable and sum-separable Lyapunov functions exist in a neighborhood of the origin if each eigenvalue of the Jacobian \(Df(0)\) has a negative real part. Results are also obtained for construction of such Lyapunov functions locally or globally, with some limitations. Various examples are provided to illustrate the constructive methods or to show the nonexistence of such functions.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 34C12
zbMATH DE Number: 6553193
zbMATH Keywords: monotone systems
zbMATH Keywords: existence of separable Lyapunov functions
zbMATH Keywords: ordinary differential equations
MaRDI profile type: Publication
full work available at URL: dcdsb.2015.20.2497
OpenAlex ID: W1059638856
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DOI: 10.3934/DCDSB.2015.20.2497
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description: scientific article; zbMATH DE number 6553193