Local stabilizability implies global controllability in catalytic reaction systems

TL;DR

This paper establishes that in certain catalytic reaction systems, the ability to locally stabilize a state guarantees the ability to globally control the system to reach that state, revealing a fundamental link between local stability and global controllability.

Contribution

It proves a general principle connecting local stabilizability to global controllability in catalytic reaction systems with matching kinetics and stoichiometry.

Findings

Local stabilizability implies global controllability within the same compatibility class.

Provides a mathematical criterion for global reachability in nonlinear chemical systems.

Highlights the robustness and controllability of biochemical reaction networks.

Abstract

Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the stoichiometric coefficient match: the local stabilizability of a given state implies global controllability within its stoichiometric compatibility class. In other words, if a target state can be maintained against small perturbations, the system can be controlled from any initial condition to that state. This result highlights a tight link between the local and global dynamics of nonlinear chemical reaction systems, providing a mathematical criterion for global reachability that is often elusive in high-dimensional systems. The finding illuminate the robustness of biochemical systems and offers a way to control catalytic reaction systems in a generic framework.