We present a framework to transform the problem of finding a Lyapunov function for a Complex 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. This is applied to reinterpret previous results on Piecewise Linear in Rates Lyapunov function, and to introduce Piecewise Quadratic in Rates Lyapunov functions for CRNs. The results are illustrated by an example.
Robust Lyapunov Functions for Complex Reaction Networks: An Uncertain System Framework / Al-Radhawi, Muhammad Ali; Angeli, David. - ELETTRONICO. - (2014), pp. 3101-3106. (Intervento presentato al convegno IEEE Conference on Decision and Control).
Robust Lyapunov Functions for Complex Reaction Networks: An Uncertain System Framework
Angeli, David
2014
Abstract
We present a framework to transform the problem of finding a Lyapunov function for a Complex 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. This is applied to reinterpret previous results on Piecewise Linear in Rates Lyapunov function, and to introduce Piecewise Quadratic in Rates Lyapunov functions for CRNs. The results are illustrated by an example.
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