Jumps of the fundamental solution matrix in discontinuous systems and applications

Abstract

This paper deals with differential equations with discontinuous right-hand side. The concept of a solution for a discontinuous system is defined on the basis of differential inclusions using Filippov’s method. We study in particular the behaviour of solutions crossing a discontinuity surface transversally. A formula characterizing jumps of the fundamental solution matrix is derived. As an application of it, the concept of Poincaré mapping is defined for such systems.