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Practical stability in terms of two measures for hybrid dynamic systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study hybrid dynamic systems on time scales. Using Lyapunov-like functions, we obtain sufficient conditions for practical stability and strict practical stability in terms of two measures for hybrid dynamic systems on time scales.
Rocznik
Strony
221--237
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
autor
autor
  • School of Science, University of Jinan, Jinan, Shandong 250022, P.R. China, sshrong@163.com
Bibliografia
  • [1] D. Acheson, From Calculus to Chaos: An Introduction to Dynamics, Oxford Univ. Press, Oxford, 1997.
  • [2] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
  • [3] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • [4] F. H. Clark, Yu. S. Ledyaev, R. I. Stern and P. R. Woleski, Nonsmooth Analysis and Control Theory, Springer, New York, 1998.
  • [5] L. T. Grujić, Exact determination of a Lyapunov function and the asymptotic stability domain, Int. J. Systems Sci. 23 (1992), 1871-1888.
  • [6] S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56.
  • [7] V. Lakshmikantham, S. Leela and A. A. Martynyuk, Practical Stability of Nonlinear Systems, World Sci., Singapore, 1990.
  • [8] V. Lakshmikantham and R. N. Mohapatra, Strict stability of differential equations, Nonlinear Anal. 46 (2001), 915-921.
  • [9] V. Lakshmikantham, S. Sivasundaram and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer, Dordrecht, 1996.
  • [10] V. Lakshmikantham and A. S. Vatsala, Hybrid systems on time scales, J. Comput. Appl. Math. 141 (2002), 227-235.
  • [11] V. Lakshmikantham and Y. Zhang, Strict practical stability of delay differential equation, Appl. Math. Comput. 118 (2001), 275-285.
  • [12] J. LaSalle and S. Lefschetz, Stability by Liapunov’s Direct Method, Academic Press, New York, 1961.
  • [13] A. M. Nerode and W. Kohn, Models for Hybrid Systems, Lecture Notes in Comput. Sci. 36, Springer, Berlin, 1993.
  • [14] P. G. Wang and X. Liu, New comparison principle and stability criteria for impulsive hybrid systems on time scales, Nonlinear Anal. Real World Appl. 7 (2006), 1096-1103.
  • [15] P. G. Wang and X. Liu Practical stability of impulsive hybrid differential systems in terms of two measures on time scales, Nonlinear Anal. 65 (2006), 2035-2042.
  • [16] P. G. Wang, M. Wu and Y. H. Wu, Practical stability in terms of two measures for discrete hybrid systems, Nonlinear Anal. Hybrid Systems 2 (2008), 58-64.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0058-0020
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