Practical Stabilization of Nonlinear Systems with Unstable Linearization

This paper studies the practical stabilization problem of a class of uncertain nonlinear systems. The systems´ Jacobian linearizations may have uncontrollable modes whose eigenvalues are in the open right half of the complex plane. By Brockett´s necessary condition, asymptotic stability cannot be achieved by a smooth static state feedback controller. We use backstepping to design a smooth static state feedback controller that achieves the weaker requirement of ultimate boundedness.