Robust Lyapunov Functions for Reaction Networks: An Uncertain System Framework

TL;DR

This paper introduces a new framework for constructing Lyapunov functions for chemical reaction networks with uncertain kinetics, linking them to linear parameter varying systems and contraction analysis.

Contribution

It provides a novel method to find Lyapunov functions for CRNs by transforming the problem into a linear parameter varying system framework, unifying previous results and analysis techniques.

Findings

Reformulation of Lyapunov function search as a linear parameter varying system problem

Connection established between Lyapunov functions and contraction analysis

Results on persistence and equilibrium uniqueness

Abstract

We present a framework to transform the problem of finding a Lyapunov function of a Chemical Reaction Network (CRN) in concentration coordinates with arbitrary monotone kinetics into finding a common Lyapunov function for a linear parameter varying system in reaction coordinates. Alternative formulations of the proposed Lyapunov function is presented also. This is applied to reinterpret previous results by the authors on Piecewise Linear in Rates Lyapunov functions, and to establish a link with contraction analysis. Persistence and uniqueness of equilibria are discussed also.