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Stability of impulsive hybrid set-valued differential wquations with delay by perturbing lyapunov functions

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EN
Abstrakty
EN
We study the stability of the zero solution of an impulsive set differential system with delay by means of the perturbing Lyapunov function method. Sufficient conditions for the stability of the zero solution of impulsive set differential equations with delay are presented.
Wydawca
Rocznik
Strony
209--218
Opis fizyczny
Bibliogr. 19 poz.
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autor
Bibliografia
  • [1] Bainov. D. D., Simeonov, P. S., Systems with Impulse Effect, Ellis Horwood, Chichester, 1989.
  • [2] Gnana Bhaskar, T., Lakshmikantham. V., Set differential equations and flow invariance, Appl. Anal. 82 (2003), 357 368.
  • [3] Gnana Bhaskar, T., Lakshmikantham. V., Lyapunov stability for set differential equation. Dynam. Systems Appl. 13 (2004). 1-10.
  • [4] Hale, J., Theory of Functional Differential Equations, Springer-Verlag, New York. 1977.
  • [5] Koksal, S., Stability properties and perturbing Lyapunov functions, J. Appl. Anal. 43 (1992), 99-107.
  • [6] Lakshmikantham, V., Bainov, D. D., Simeonov. P. S., Theory of Impulsive Differential Equations, World Scientific Publishing Co., Inc., Teaneck, NJ, 1989.
  • [7] Lakshmikantham, V., Gnana Bhaskar, T., Devi. J. V.. Theory of Set Differential Equations, Cambridge Scientific Publishers, Cambridge, 2006.
  • [8] Lakshmikantham, V., Leela, S., On perturbing Lyapunov functions, Math. Systems Theory 10 (1976), 85-90.
  • [9] Lakshmikantham, V., Leela, S., Vatsala, A. S.. Set-valued hybrid differential equations and stability in terms of two measures, Internal. J. Hybrid Systems 2 (2002), 169 187.
  • [10] Lakshmikantham, V., Leela, S., Vatsala, A. S., Interconnection between set, and fuzzy differential equations, Nonlinear Anal. 54 (2003), 351-360.
  • [11] Lakshmikantham, V., Leela, S., Vatsala, A. S., Stability theory for set differential. equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 11 (2004). 181-189.
  • [12] Lakshmikantham, V., Matrosov, V. M., Sivasundaram, S.. Vector Lyapunov Functions and Stability Analysis of Nonlinear Systems, Kluwer Academic Publishers. Dordrecht, 1991.
  • [13] Lakshmikantham, V., Tolstonogov, A., Existence and interrelation between set and fuzzy differential equations. Nonlinear Anal. 55 (2003), 255-268.
  • [14] Lopes Pinto, A. J. Brandao, De Blasi, F. S., Iervolino, F., Uniqueness and existence theorems for differential equations with compact convex valued solutions. Boll. Un. Mat. Ital. (4) 3 (1970), 47-54.
  • [15] McRae, F. A., Devi, J. V., Impulsive set differential equations with delay. Appl. Anal. 84 (2005), 329-341.
  • [16] Samoilenko. A. M., Perestyuk, N. A., Impulsive Differential Equations, World Scientific Publishing Co., Inc., River Edge, NJ, 1995.
  • [17] Soliman, A. A., Lipschitz stabilty with perturbing Lyapunov functionals, Appl. Math. Lett. 17 (2004), 939-944.
  • [18] Stutson, D., Vatsala A. S., Composite boundedness and stability results by perturbing Lyapunov functions, Nonlinear Anal. 26 (1996), 761-766.
  • [19] Tolstonogov, A., Differential Inclusions in a, Banach Space, Kluwer Academic Publishers, Dordrecht, 2000.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD6-0006-0024
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