Space design for the multilayer minimum projection method in nonsmooth control Lyapunov function design

This paper considers a non-smooth control Lyapunov function (CLF) design problem for global asymptotic stabilization of a system defined on a manifold. This problem can be addressed by the multilayer minimum projection method with singular point assignment, which considers manifolds, called multilayered spaces, different from those where the control system is originally defined. This requires a multilayered space satisfying specific conditions. However, a design method for the required space has not previously been provided. In this paper, we propose a design method for a multilayered space guaranteed to satisfy the required conditions using the concept of a multigraph and apply it in a robot navigation example.