On the global polynomial stabilization of nonlinear dynamical systems

This paper presents new criteria for the rational stability of dynamical systems. We introduce basic and useful results on how to construct control laws to assure rational stability. Both Coron and Sontag examples were re-visited. A particular attention is paid to time-varying systems where sufficient Lyapunov conditions are developed guaranteeing the rational stability of this class of systems. As application, the example of double integrator is treated where new time-varying feedbacks rationally stabilizing this system are reconstructed.