Stabilization of time delayed nonnegative polynomial systems through kinetic realization

A new stabilizing feedback design method is proposed in this paper for time delayed nonnegative polynomial systems with a linear input structure. Using a polynomial state feedback, the open loop system is transformed into a complex balanced kinetic system that is known to be stable with a known Lyapunov-Krasovskii functional. The computation problem is solved through semidefinite programming exploiting the fact that the reaction graph structure and weighting of a kinetic polynomial system are non-unique.