Original scientific paper

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

Nataša A. Kablar ; Lola Institute, Faculty of Computer Science, University of Belgrade, Belgrade, Serbia
Vladimir Kvrgić ; Lola Institute, Belgrade, Serbia
Dragutin Lj. Debeljković ; Faculty of Mechanical Engineering, University of Belgrade, Belgrade, Serbia

Abstract

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.

Keywords

singular systems; singularly impulsive dynamical systems; time delay; mathematical model; stability

Hrčak ID:

111269

URI

https://hrcak.srce.hr/111269

Publication date:

29.11.2013.

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