Singularly Impulsive Dynamical Systems with Time Delay: Razumikhin Stability

Natasa Kablar, Vladimir Kvrgi´c, Mirko Bu´can, Dragutin Lj. Debeljkovi´c

Abstract


In this paper we introduce new class of system, so called singularly impulsive or generalized impulsivedynamical systems with time delay. Dynamics of this system is characterized by the set of differential and differenceequations with time delay, and algebraic equations. They represent the class of hybrid systems, where algebraic equationsrepresent constraints that differential and difference equations with time delay need to satisfy. In this paper we presentmodel, assumptions on the model, and two classes of singularly impulsive dynamical systems with delay - time dependentand state dependent. Further, we present Lyapunov - Krasovskii and Razumikhin stability results for the class of singularlyimpulsive dynamical systems with time delay.

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References


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