New approach to the stability of chemical reaction networks: piecewise linear in rates Lyapunov functions
File(s)
Accepted version
Author(s)
Al-Radhawi, MA
Angeli, D
Type
Journal Article
Abstract
Piecewise-linear in rates (PWLR) Lyapunov functions are introduced for a class of chemical reaction networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of which Mass-Action is a special case. The existence of such functions ensures the convergence of trajectories towards equilibria, and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class. We give the definition of these Lyapunov functions, prove their basic properties, and provide algorithms for constructing them. Examples are provided, relationship with consensus dynamics are discussed, and future directions are elaborated.
Date Issued
2016-01
Date Acceptance
2015-04-29
Citation
IEEE Transactions on Automatic Control, 2016, 61 (1), pp.76-89
ISSN
1558-2523
Publisher
IEEE
Start Page
76
End Page
89
Journal / Book Title
IEEE Transactions on Automatic Control
Volume
61
Issue
1
Copyright Statement
© 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Sponsor
The Leverhulme Trust
Grant Number
F/07/058/BU
Subjects
Science & Technology
Technology
Automation & Control Systems
Engineering, Electrical & Electronic
Engineering
Biochemical networks
chemical reaction networks (CRNs)
Lyapunov methods
robust stability
MASS-ACTION KINETICS
SYSTEMS
INJECTIVITY
CONSENSUS
Industrial Engineering & Automation
0906 Electrical And Electronic Engineering
0102 Applied Mathematics
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2015-04-29