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

Abstract

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

Nonlinear Nonsingular Fast Terminal Sliding Mode Control Using Deep Deterministic Policy Gradient

“…Therefore, when e 2 = 0 is applied, the controller satisfies Lyapunov stability condition [34] and has good stability and robustness. The system will arrive at sliding mode surface in finite time.…”