Robust Lyapunov Functions for Reaction Networks: An Uncertain System Framework

2015/09/07 by M. Ali Al-Radhawi, David Angeli, Al-Radhawi, M. Ali +1
Engineering · Biochemistry, Genetics and Molecular Biology · #Control and Stability of Dynamical Systems #Gene Regulatory Network Analysis #Advanced Control Systems Optimization

paper · pdf · doi:10.48550/arxiv.1509.02086

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.

Citations

• General mass action kinetics

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