Homogeneous Stabilization for Input Affine Homogeneous Systems

Dilated homogeneous systems are local canonical forms of nonlinear control systems. For input affine homogeneous systems, existence of continuous homogeneous stabilizing controllers is equivalent to existence of differentiable homogeneous control Lyapunov functions. In this technical note, we propose an homogeneous stabilizing controller and an homogeneous inverse optimal controller for multi-input affine homogeneous systems with given homogeneous control Lyapunov functions.