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— 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.(More)
— Singularly impulsive (or generalized impulsive) dynamical systems are systems which dynamics are 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. For the class of nonlinear(More)
In this paper we present finite-time stability results for nonlinear singularly impulsive dynamical systems by using quasi-Lyapunov function approach. Motivated by the results on impulsive dynamical systems presented in Haddad, Chellaboina, and Kablar (2001a-b) and Haddad, Kablar, Chellaboina (2000, 2005) and the authors previous work on singular or(More)
In this paper we develop dissipativity results for discrete nonlinear and linear singular systems. To the best knowledge of author results are nonexistent. We generalize dissipativity theory to discrete nonlinear singular dynamical systems. Specifically, the classical concepts of system storage functions and supply rates are extended to singular dynamical(More)
— In this paper for the class of nonlinear uncertain singularly impulsive dynamical systems we present optimal robust control and inverse robust optimal control results. We consider a control problem for nonlinear uncertain singularly impulsive dynamical systems involving a notion of optimality with respect to an auxiliary cost which guarantees a bound on(More)
In this paper we introduce new class of system , so called singularly impulsive or generalized impulsive dynamical systems with time delay. Dynamics of this system is characterized by the set of differential and difference equations with time delay, and algebraic equations. They represent the class of hybrid systems, where algebraic equations represent(More)
Singularly impulsive (or generalized impulsive) dynamical systems are systems which dynamics are 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. For the class of singularly(More)
In this paper we present mathematical model of well known Delta-Notch signaling system in form of nonlinear, singular, impulsive and singularly impulsive dynamical systems. This example is interesting since it posses phenomena of lateral inhibition recognized to be underlying element in mechanism structures in many living organisms. It is characterized by(More)
In this paper we present singular and singularly impulsive model of genetic regulatory networks. Concrete example consists of two gene — two proteins simple synthetic network, and posses two fundamentally present parts in biochemical networks — positive and negative feedback loops. These are important structural parts of biochemical networks(More)
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