Kinetic feedback computation for polynomial systems to achieve weak reversibility and minimal deficiency

In this paper, an optimization based state feedback design is proposed for polynomial models that transforms an open-loop system into weakly reversible kinetic form with minimal deficiency, if possible. Therefore, the suggested method is able to decide whether the deficiency zero property and weak reversibility of the closed loop system (that guarantees a robust stability property) is achievable by the given feedback structure. The approach integrates feedback design and previous computational methods for computing dynamically equivalent realizations of kinetic systems. The method assumes a linear input structure of the open loop system, and uses a polynomial feedback constructed from the monomials of the original system possibly extended by new ones. The proposed method is illustrated on two simple examples.