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Practical Stability with Respect to h -Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations

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  • Gani Stamov

    (Department of Mathematics and Physics, “Prof. Dr. Assen Zlatarov” University, 8010 Burgas, Bulgaria
    Current address: Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA.
    These authors contributed equally to this work.)

  • Ivanka Stamova

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
    These authors contributed equally to this work.)

  • Xiaodi Li

    (School of Mathematics and Statistics, Shandong Normal University, Ji’nan 250014, China
    These authors contributed equally to this work.)

  • Ekaterina Gospodinova

    (Department of Mathematics and Physics, “Prof. Dr. Assen Zlatarov” University, 8010 Burgas, Bulgaria
    These authors contributed equally to this work.)

Abstract

The present paper is devoted to the problems of practical stability with respect to h -manifolds for impulsive control differential equations with variable impulsive perturbations. We will consider these problems in light of the Lyapunov–Razumikhin method of piecewise continuous functions. The new results are applied to an impulsive control cellular neural network model with variable impulsive perturbations.

Suggested Citation

  • Gani Stamov & Ivanka Stamova & Xiaodi Li & Ekaterina Gospodinova, 2019. "Practical Stability with Respect to h -Manifolds for Impulsive Control Functional Differential Equations with Variable Impulsive Perturbations," Mathematics, MDPI, vol. 7(7), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:656-:d:250382
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    References listed on IDEAS

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    1. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    2. Xinzhi Liu & Allan R. Willms, 1996. "Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft," Mathematical Problems in Engineering, Hindawi, vol. 2, pages 1-23, January.
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