Compound Lyapunov type functions in control problems of impulsive dynamical systems

The paper is devoted to the study of impulsive dynamical systems with trajectories of bounded variation and impulsive controls (regular vector measures). In the paper, strongly monotone Lyapunov type functions relative to impulsive control system are introduced and infinitesimal conditions of the strong monotonicity of Lyapunov type functions are presented. We focus mainly on the study of compound (defined piecewise in the variable t) Lyapunov type functions, which are more applicable for dynamical systems with discontinuous trajectories, and give their applications to outer estimations of the reachable sets.