Construction of nonpathological Lyapunov functions for discontinuous systems with Caratheodory solutions

Abstract

This paper presents a method based on the Nonpathological Lyapunov theorem for constructing Lyapunov function (LF) for discontinuous time invariant dynamical systems with Caratheodory solutions. The origin is stable, if the method constructs a Nonpathological Lyapunov Function (NPLF) for the system.

Multilayer Minimum Projection Method with Singular Point Assignment for Nonsmooth Control Lyapunov Function Design

“…Extension of the method to infinite‐dimensional systems (particularly to Lyapunov Krasovskii or Razumikhin functionals) will be a challenge. Further, patchy control Lyapunov function and nonpathological Lyapunov functions are also related topics. Comparison of the minimum projection method with these Lyapunov functions also remains future work.…”

On the Boundedness of Solutions of Discontinuous Differential Equations

“…Ordinary differential equations with the discontinuous right side, also called discontinuous differential equations, determine discontinuous systems. The boundedness of solutions to discontinuous systems determined by autonomous differential equations was studied by [2].…”