2014•Carpathian Journal of MathematicsOpen access

Control of systems with Holder continuous functions in the distributed delays

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Abstract

An exponential stabilization result is proved for a doubly nonlinear distributed delays system of ordinary differential equations. The problem involves non-Lipschitz continuous distributed delays of non-Lipschitz continuous ”activation” functions. This extends similar previous works where the distributed delays as well as the activation functions were assumed to be Lipschitz continuous.

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An exponential stabilization result is proved for a doubly nonlinear distributed delays system of ordinary differential equations. The problem involves non-Lipschitz continuous distributed delays of non-Lipschitz continuous ”activation” functions. This extends similar previous works where the distributed delays as well as the activation functions were assumed to be Lipschitz continuous.

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Available abstract

An exponential stabilization result is proved for a doubly nonlinear distributed delays system of ordinary differential equations. The problem involves non-Lipschitz continuous distributed delays of non-Lipschitz continuous ”activation” functions. This extends similar previous works where the distributed delays as well as the activation functions were assumed to be Lipschitz continuous.

Key concepts: Lipschitz continuity, Ordinary differential equation, Hölder condition, Control theory (sociology), Nonlinear system, Exponential function, Mathematics, Control (management)

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