On state accessibility in reaction systems

Reaction systems constitute a class of nonlinear dynamical systems relevant in many engineering fields such as chemical engineering, biotechnology, and ecology. A detailed presentation of reaction systems is given including a description of reaction networks, the main assumptions regarding the reaction kinetics and the exchange dynamics and the derivation of a general state-space model. Simple algebraic criteria are presented for the direct computation of the strong accessibility rank of reaction systems, from the knowledge of the reaction network structure only. It is shown that, in case where the system is generically not full state accessible, the uncontrollable modes are necessarily governed by stable linear dynamics, in appropriate coordinates