- ▪D. Angeli, P. de Leenheer, E.D. Sontag, "Chemical networks with inflows and outflows: A positive linear differential inclusions approach", Biotechnology Progress, vol. 25, pp. 632-642, 2009. pdfreaction networks · fluxes · differential inclusions · positive systems · Petri nets · persistence · switched systems
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 biochemical reaction networks with inflows and outflows. Included is also a characterization of exponential stability of general homogeneous switched systems
- ▪D. Angeli, B.P. Ingalls, E.D. Sontag, Y. Wang, "Uniform global asymptotic stability of differential inclusions", J. Dynam. Control Systems, vol. 10, no. 3, pp. 391–412, 2004. doipdf
Abstract
The stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not necessarily convex) valued differential inclusions. The main result is presented in a context which is useful for control-theoretic applications: a differential inclusion with two outputs is considered, and the result applies to the property of global error detectability.