Brief paperÉtale backstepping for control Lyapunov function design on manifold

Backstepping is one of the most popular nonlinear controller and differentiable control Lyapunov function (CLF) design techniques. However, for asymptotic stabilization of systems defined on noncontractible manifolds, there exists no differentiable CLF; the semiconcave CLF design problem based on the backstepping has not been discussed. In this paper, we propose a backstepping based controller design method for asymptotic stabilization of systems defined on noncontractible manifolds. In the method, we design a controller and a CLF on an étale space. Then, we obtain a semiconcave CLF on the original space by the minimum projection method. The effectiveness of the proposed method is confirmed by computer simulation.