Stabilizing kinetic feedback design using semidefinite programming

A novel state feedback design method is proposed in this paper for the stabilization of polynomial systems with linear input structure. Using a static nonlinear feedback, the open loop system is transformed to a complex balanced kinetic closed loop system with stoichiometric subspace having maximum dimension, that is known to be stable. The feedback law is computed using semidefinite programming where the objective function is used to adjust the performance of the closed-loop system by tuning the largest eigenvalue of the state matrix of the linearized closed-loop system. The approach is illustrated on a purely computational example followed by a simple process system example.