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A converse theorem on $h$-stability via impulsive variational systems

Namjip Koo|Sung Kyu Choi
대한수학회 (The Korean Mathematical Society)|2016.09|대한수학회지 (Journal of the KMS)|제53권 제5호|pp. 1115-1131

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참고문헌

키워드

$h$-stabilityimpulsive variational systemsimpulsive differential systems$t_\infty$-similarityconverse stability theorem
주제분류수학

초록

In this paper we develop useful relations which estimate the difference between the solutions of nonlinear impulsive differential systems with different initial values. Then we obtain the converse $h$-stability theorem of Massera's type for the nonlinear impulsive systems by employing the $t_\infty$-similarity of the associated impulsive variational systems and relations.

Abstract

In this paper we develop useful relations which estimate the difference between the solutions of nonlinear impulsive differential systems with different initial values. Then we obtain the converse $h$-stability theorem of Massera's type for the nonlinear impulsive systems by employing the $t_\infty$-similarity of the associated impulsive variational systems and relations.

참고문헌 (22)

  1. D. D. Bainov, "Kinematical similarity and exponential dichotomy of linear abstract impulsive differential equations", Internat. J. Theoret. Phys, 33(2), pp.487~497 (1994)
  2. D. D. Bainov, "Systems with Impulse Effect: Stability, Theory and Applications" (1989), Ellis Horwood Limited
  3. D. D. Bainov, "Impulsive Differential Equations: Asymptotic Properties of the Solutions" (1995), World Scientific Publishing Co
  4. S. K. Choi, "Variationally stable impulsive differential systems", Dyn. Syst, 30(4), pp.435~449 (2015)
  5. 최성규, "h-stability of linear impulsive differential equations via similarity", 충청수학회지, 24(2), pp.393~400 (2011), 충청수학회
  6. 최성규, "Stability of linear impulsive differential equations via t∞-similarity", 충청수학회지, 26(4), pp.811~819 (2013), 충청수학회[DOI]
  7. S. K. Choi, "h-Stability of differential systems via t∞-similarity", Bull. Korean Math. Soc, 34(3), pp.371~383 (1997)
  8. R. Conti, "Sulla t∞-similitudine tra matrici e la stabilita´ dei sistemi differenzialelineari", Atti. Acc. Naz. Lincei, Rend. Cl. Fis. Mat. Nat, 19, pp.247~250 (1955)
  9. F. M. Dannan, "Lipschitz stability of nonlinear systems of differential equations", J. Math. Anal. Appl, 113(2), pp.562~577 (1986)
  10. J. V. Devi, "A variation of the Lyapunov second method to impulsive differential equations", J. Math. Anal. Appl, 177(1), pp.190~200 (1993)
  11. M. Dlala, "Uniform exponential practical stability of impulsive perturbed systems", J. Dyn. Control Syst, 13(3), pp.373~386 (2007)
  12. G. K. Kulev, "Lipschitz stability of impulsive systems of differential equations", Internat. J. Theoret. Phys, 30(5), pp.737~756 (1991)
  13. V. Lakshmikantham, "Theory of Impulsive Differential Equations" (1989), World Scientific Publishing Co
  14. V. Lakshmikantham, "Method of Variation of Parameters for Dynamical Systems" (1998), Gordon and Breach Science Publishers
  15. V. Lakshmikantham, "Differential and Integral Inequalities, Vol I and II" (1969), Academic Press
  16. R. Medina, "Uniform asymptotic stability of solutions of impulsive differential equations", Dynam. Systems Appl, 5(1), pp.97~107 (1996)
  17. M. Pinto, "Perturbations of asymptotically stable differential systems", Analysis, 4(1-2), pp.161~175 (1984)
  18. M. Pinto, "Stability of nonlinear differential systems", Appl. Anal, 43(1-2), pp.1~20 (1992)
  19. P. S. Simeonov, "Stability of the solutions of singularly perturbed systems with impulse effect", J. Math. Anal. Appl, 136(2), pp.575~588 (1988)
  20. P. S. Simeonov, "Exponential stability of the solutions of singularly perturbed systems with impulse effect", J. Math. Anal. Appl, 151(2), pp.462~487 (1990)
  21. J. Shen, "Global existence results for impulsive differential equations", J. Math. Anal. Appl, 314(2), pp.546~557 (2006)
  22. T. Yoshizawa, "Stability Theory by Liapunov’s Second Method" (1966), The Mathematical Society of Japan

관련 논문AI추천

ON STABILITY OF LINEAR IMPULSIVE SYSTEMS강보원, 구남집, 최성규장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2016 · 제19권 제4호On stability of nonlinear integro-differential systems with impulsive effect강보원, 구남집, 이현희대한수학회 · 대한수학회논문집2020 · 제35권 제3호Boundedness in nonlinear perturbed differential systems via $t_{\infty}$-similarity구윤회, 임동만강원경기수학회 · 한국수학논문집2016 · 제24권 제4호h-STABILITY OF PERTURBED DIFFERENTIAL SYSTEMS구윤회한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제4호h¡STABILITY OF NONLINEAR PERTURBED DIFFERENTIAL SYSTEMS VIA t1-SIMILARITY구윤회, 양승범한국수학교육학회 · 이론수학과 교직수학2012 · 제19권 제2호Boundedness in Perturbed functional differential systems via $t_{\infty}$-similarity구윤회, 최상일강원경기수학회 · 한국수학논문집2015 · 제23권 제2호

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