On Stability Analysis of Non-Smooth Systems with Density Functions

This study discusses a condition of the stability with density functions, which is known as a dual theorem of the Lyapunov stability theorem, for non-smooth dynamical systems. In the previous study, the stability analysis can be applied only for smooth systems. The aim of this study is to relax the smoothness conditions to develop the analysis for non-smooth dynamical systems, which would appear in global stabilization problems of nonlinear systems and the analysis of the finite-time stability. To this end, we develop an extension of a density function approach for non-smooth systems. We focus on a class of non-smooth systems and we show the stability analysis of non-smooth systems for the class of the systems with density functions. We also provide numerical examples to show the validness of the presented results.