A Balanced Shaping Method for Stabilizing Chemical Reaction Networks

A balanced shaping method for stabilizing open mass action systems is proposed in this paper. Since complex balanced systems are locally asymptotically stable, the closed loop system, which is dynamically equivalent to a complex balanced system under state feedback, is also stable. Essentially, the stabilization process is to find a target system such that the matching equation is satisfied. We show that balanced shaping control is an equivalent method of kinetic feedback design for stabilizing open mass action systems. In addition, controller design based on solving convex quadratic programming is also presented. Lastly, we illustrate the effectiveness of balanced shaping control with two examples.