Practical Stabilization of Nonlinear Systems with Unstable Linearization

Abstract

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.