Stabilization of nonlinear affine systems by homogeneous method

In this paper, we consider the stabilization problems for nonlinear affine systems based on homogeneous control Lyapunov function. There are two main results. The first one is that we propose a feedback controller for a kind of nonlinear multi-input affine system by using a control Lyapunov function. The other is that, by applying the homogeneous properties, we derive the sufficient conditions for the continuity of the proposed controller. An academic example is given to verify the effectiveness of the method.