A duality-based LPV approach to polynomial state feedback design

In this paper, a state feedback design for the class of polynomial control systems is proposed. The proposed design solves the stabilization problem by considering polynomial control systems as linear parameter varying (LPV) control systems. With the help of duality theory and the sum of squares decomposition, a stabilizing state feedback can be computed efficiently, if a certain semidefinite program is feasible. The main advantages of the proposed state feedback design are that no special requirements on the system structure are imposed and that the results are of global nature.