Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular

DOI10.1016/j.automatica.2017.08.022zbMath1375.93098OpenAlexW2758156712MaRDI QIDQ1678628

Franco Blanchini, Giulia Giordano

Publication date: 17 November 2017

Published in: Automatica (Search for Journal in Brave)

Full work available at URL: http://resolver.tudelft.nl/uuid:54ccffe9-9a2e-4608-a632-76d3c74d26f2

zbMATH Keywords

global stabilitystructural stabilitychemical reaction networksdynamical networkspiecewise-linear Lyapunov functions

Mathematics Subject Classification ID

Lyapunov and storage functions (93D30) Decentralized systems (93A14) Asymptotic stability in control theory (93D20)

Related Items (7)

Structural analysis in biology: a control-theoretic approach ⋮ Vertex results for the robust analysis of uncertain biochemical systems ⋮ Graphical characterizations of robust stability in biological interaction networks ⋮ Adaptive control of nonlinear impulsively coupled complex networks with mismatching conditions ⋮ Convergence in uncertain linear systems ⋮ The deficiency zero theorem and global asymptotic stability for a class of chemical reaction networks with arbitrary time delays ⋮ Michaelis-Menten networks are structurally stable

Cites Work

• Unnamed Item
• Unnamed Item
• Computing the structural influence matrix for biological systems
• Piecewise-linear Lyapunov functions for structural stability of biochemical networks
• Engineering model reduction and entropy-based Lyapunov functions in chemical reaction kinetics
• Constrained control for uncertain linear systems
• Criteria of asymptotic stability of differential and difference inclusions encountered in control theory
• A fixed point theorem for bounded dynamical systems
• The existence and uniqueness of steady states for a class of chemical reaction networks
• Multiple steady states for chemical reaction networks of deficiency one
• On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics
• New Approach to the Stability of Chemical Reaction Networks: Piecewise Linear in Rates Lyapunov Functions
• Global Asymptotic Stability for a Class of Nonlinear Chemical Equations
• On rest points of dynamical systems
• Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction
• Diffeomorphisms with Banach space domains
• Multiple Equilibria in Complex Chemical Reaction Networks: I. The Injectivity Property
• Multiple Equilibria in Complex Chemical Reaction Networks: II. The Species-Reaction Graph
• Set-theoretic methods in control

This page was built for publication: Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular