Singularly impulsive or generalized impulsive dynamical systems: Lyapunov and asymptotic stability

In this paper we present singularly impulsive or generalized impulsive dynamical systems. Dynamics of this system is characterized by the set of differential, difference, and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent constraints that differential and difference equations need to satisfy. Generalized term have as source generalized systems theory where singular system theory can be viewed as generalization of regular system theory. For this class of system we develop Lyapunov and asymptotic stability theorems.