Monotonicity of Lyapunov Type Functions for Measure-Driven Differential Systems
This paper deals with impulsive dynamical
systems with trajectories of bounded variation and impulsive controls (regular vector measures). Definitions of strong and weak monotonicity and
$V$-monotonicity of Lyapunov type functions
with the corresponding infinitesimal conditions in the form of
Hamilton--Jacobi proximal or differential inequalities are proposed and discussed.