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ON LYAPUNOV-TYPE FUNCTIONS FOR LINEAR DYNAMIC EQUATIONS ON TIME SCALES

  • Choi, Sung Kyu (Department of Mathematics Chungnam National University) ;
  • Cui, Yinhua (Department of Applied Mathematics Paichai University) ;
  • Koo, Namjip (Department of Mathematics Chungnam National University) ;
  • Ryu, Hyun Sook (Department of Mathematics Chungnam National University)
  • Published : 2012.02.15

Abstract

In this paper we give a necessary and sufficient condition for characterizing $h$-stability for linear dynamic systems on time scales by using Lyapunov functions.

Keywords

References

  1. R. P. Agarwal, Difference Equations and Inequalities, 2nd ed., Marcel Dekker, New York, 2000.
  2. M. Bohner and A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhauser, Boston, 2001.
  3. S. Elaydi, An Introduction to Difference Equations, third ed., Springer, New York, 2005.
  4. S. K. Choi, N. J. Koo, and H. S. Ryu, h-stability of differential systems via $t{\infty}$-similarity, Bull. Korean Math. Soc. 34 (1997), 371-383.
  5. S. K. Choi and N. J. Koo, Variationally stable difference systems by $n{\infty}$-similarity, J. Math. Anal. Appl. 249 (2000), 553-568. https://doi.org/10.1006/jmaa.2000.6910
  6. S. K. Choi, N. J. Koo, and D. M. Im, h-stability for linear dynamic equations on time scales, J. Math. Anal. Appl. 324 (2006), 707-720. https://doi.org/10.1016/j.jmaa.2005.12.046
  7. P. E. Kloeden and A. Zmorzynska, Lyapunov functions for linear nonautonomous dynamical equations on time scales, Adv. Differ. Equ. 2006 (2006), Article ID 69106, pages 1-10.
  8. V. Lakshmikantham and S. Leela, Differential and Integral Inequalites with Theory and Applications, Academic Press, New York and London, 1969.
  9. A. M. Lyapunov, The general problem of the stability of motion, Internat. J. Control 55 (1992), no. 3, 521-790. https://doi.org/10.1080/00207179208934252
  10. V. Lakshmikantham, S. Sivasundaram, and B. Kaymakcalan, Dynamic Systems on Measure Chains, Kluwer Academic Publishers, Boston, 1996.
  11. R. Medina and M. Pinto, Stability of nonlinear difference equations, Proc. Dynamic Systems and Appl. 2 (1996), 397-404.
  12. M. Pinto, Perturbations of asymptotically stable differential systems, Analysis 4 (1984), 161-175.
  13. T. Yoshizawa, Stability Theory by Liapunov's Second Method, The Mathematical Society of Japan, 1966.

Cited by

  1. BOUNDEDNESS FOR PERTURBED DIFFERENTIAL EQUATIONS VIA LYAPUNOV EXPONENTS vol.25, pp.3, 2012, https://doi.org/10.14403/jcms.2012.25.3.589