A New Stabilizing Control for A Class of Nonlinear Systems

This paper considers the stabilization problem of systems that have a linear part and a nonlinear part satisfying the Lipschitz condition. This paper proposes linear controls to stabilize such nonlinear systems. When the linear part of nonlinear system is non-minimum phase, the linear control is based on an H-infinity -like Riccati equation. When the linear part is minimum phase, the linear control is based on an LQ Riccati equation. The proposed control design does not require knowledge of the nonlinear function, and is shown to be globally stabilizing. A simulation example is given to verify the proposed control.