What can linear state feedback accomplish for nonlinear systems?

The purpose of this paper is to address the important question of when an uncertain system with higher-order nonlinearities can be effectively controlled by linear state feedback. In particular, for a family of uncertain nonlinear systems whose linearization is usually uncontrollable or, even worse, has uncontrollable modes associated with eigenvalues on the right-half plane, there is no linear or smooth state feedback to achieve global asymptotic stabilization (GAS). However, we show that if a less aggressive control objective such as semi-global asymptotic stabilization (SGAS) or semi-global practical stabilization (SGPS) is sought, linear controllers would be sufficient and meet the control goal. Several examples are provided to illustrate the effectiveness of the proposed robust linear state feedback control laws.