SINGULARLY IMPULSIVE DYNAMICAL SYSTEMS WITH TIME DELAY: MATHEMATICAL MODEL AND STABILITY

In this paper we introduce a new class of systems, the so-called singularly impulsive or generalized impulsive dynamical systems with time delay. Dynamics of these systems is characterized by a set of differential and difference equations with time delay, and by algebraic equations. They represent a class of hybrid systems where algebraic equations represent constraints that differential and difference equations with time delay need to satisfy. In this paper we present a model, assumptions about the model, and two classes of singularly impulsive dynamical systems with delay time-dependent and state-dependent. Further, we present the Lyapunov and asymptotic stability theorems for nonlinear time-dependent and state-dependent singularly impulsive dynamical systems with time delay.