Input-to-State Stability of Rate-Controlled Biochemical Networks

In this paper, the study of the class of biochemical systems known as zero deficiency networks is extended to the case of time-varying kinetic parameters. We show that the resulting class of nonlinear systems with inputs satisfies a notion of input-to-state stability uniformly over a set of parameters. In particular, the input-to-state stability estimates allow us to characterize the robustness of zero deficiency networks with respect to perturbations in the parameters as well as study their stability when the reaction rates are controlled by an independent process.