Chemical networks with inflows and outflows: A positive linear differential inclusions approach
David Angelia b c✉, Patrick De Leenheerd, Eduardo D. Sontage
- aDept. of Electrical and Electronic Engineering, Imperial College, London, UK. angeli@dsi.unifi.it
- bDept. of Electrical and Electronic Engineering, Imperial College, London, U.K
- cDip. di Sistemi e Informatica, University of Firenze, Firenze, Italy
- dDep. of Mathematics, University of Florida, Gainesville, FL 32611
- eDep. of Mathematics, Rutgers University, Piscataway, NJ 08854
- ✉Corresponding author
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Abstract
Certain mass-action kinetics models of biochemical reaction networks, although described by nonlinear differential equations, may be partially viewed as state-dependent linear time-varying systems, which in turn may be modeled by convex compact valued positive linear differential inclusions. A result is provided on asymptotic stability of such inclusions, and applied to a ubiquitous biochemical reaction network with inflows and outflows, known as the futile cycle. We also provide a characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle.
TL;DRA characterization of exponential stability of general homogeneous switched systems which is not only of interest in itself, but also plays a role in the analysis of the futile cycle. (Semantic Scholar)