Asymptotic stabilization of nonlinear systems on general manifolds via minimum projection method

Asymptotic stabilization on noncontractible manifolds is known as a difficult control problem. For the problem, we proposed the minimum projection method to design a nonsmooth control Lyapunov function on a manifold. However, how to stabilize the control system defined on the manifold with the obtained control Lyapunov function remains a problem. Then, a Rifford-type formula on general manifolds is proposed with nonsmooth control Lyapunov functions via the minimum projection method in this paper. Moreover, we prove our proposed method asymptotically stabilize the origin of the control system defined on the manifold in the sense of Euler and π-trajectory. The effectiveness of the proposed method is illustrated by an example of collision avoidance of a mobile robot.