Numerical design of Lyapunov functions for a class of homogeneous discontinuous systems

This paper deals with the analytical and numerical design of a Lyapunov function for homogeneous discontinuous systems. First, presented converse theorems provide two analytic expressions locally Lipschitz continuous functions systems negative homogeneity degree, generalizing classical results. Second, methodology construction those is extended to class under consideration. Finally, developed theory applied some higher-order sliding mode algorithms.