New results on global exponential stabilization of impulsive functional differential equations with infinite delays or finite delays

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 5, 2010, Pages 4194-4201

  Li, Xiaodi ^a  

^a XIAMEN UNIVERSITY   (China)

Author keywords

Finite delays; Global exponential stabilization; Improved Razumikhin technique; Impulsive functional differential equations; Infinite delays; Lyapunov functions

Indexed keywords

GLOBAL EXPONENTIAL STABILIZATION; IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATION; IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS; INFINITE DELAY; RAZUMIKHIN TECHNIQUE;

CHAOTIC SYSTEMS; CONTROL SYSTEM STABILITY; EXPONENTIAL FUNCTIONS; LYAPUNOV FUNCTIONS; STABILIZATION;

DIFFERENTIAL EQUATIONS;

EID: 77955516109     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.05.006     Document Type: Article

References (38)

1. K. Gopalsamy, and B. Zhang On delay differential equations with impulses J. Math. Anal. Appl. 139 1989 110 122
2. A. Anokhin On linear impulse systems for functional differential equations Soviet Math. Dokl. 33 1986 220 223
3. A. Ignatyev On the stability of invariant sets of systems with impulse effect Nonlinear Anal. 69 2008 53 72
4. I. Stamova Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations J. Math. Anal. Appl. 325 2007 612 623
5. X. Liu, and Q. Wang The method of Lyapunov functionals and exponential stability of impulsive systems with time delay Nonlinear Anal. 66 2007 1465 1484 (Pubitemid 46072680)
6. Q. Wang, and X. Liu Impulsive stabilization of delay differential systems via the LyapunovRazumikhin method Appl. Math. Lett. 20 2007 839 845 (Pubitemid 46529125)
7. J. Yan, and J. Shen Impulsive stabilization of functional differential equations by LyapunovRazumikhin functions Nonlinear Anal. 37 1999 245 255
8. X. Fu, and X. Li W -stability theorems of nonlinear impulsive functional differential systems J. Comput. Appl. Math. 2008 33 46
9. M. Benchohra, J. Henderson, and S. Ntouyas Impulsive Differential Equations and Inclusions 2006 Hindawi Publishing Corporation New York
10. A. Samoilenko, and N. Perestyuk Impulsive Differential Equations 1995 World Scientific Singapore
11. S. Zavalishchin, and A. Sesekin Dynamic Impulse Systems. Theory and Applications Mathematics and its Applications vol. 394 1997 Kluwer Academic Publishers Group Dordrecht
12. J.J. Nieto, and D. O'Regan Variational approach to impulsive differential equations Nonlinear Anal. RWA 10 2009 680 690
13. J.J. Nieto, and R. Rodriguez-Lopez Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations J. Math. Anal. Appl. 318 2006 593 610
14. J.J. Nieto, and C.C. Tisdell On exact controllability of first-order impulsive differential equations Adv. Difference Equ. 2010 2010 9 pages Article ID 136504
15. V. Lakshmikantham, L. Wen, and B. Zhang Theory of Differential Equations with Unbounded Delay Mathematics and its Applications 1994 Kluwer Academic Publishers Dordrecht
16. X. Fu, B. Yan, and Y. Liu Introduction of Impulsive Differential Systems 2005 Science Press Beijing
17. J. Shen Existence and uniqueness of solutions for a class of infinite delay functional differential equations with applications to impulsive differential equations J. Huaihua Teach. Coll. 15 1996 45 51 (in Chinese)
18. A. Ouahab Existence and uniqueness results for impulsive functional differential equations with scalar multiple delay and infinite delay Nonlinear Anal. 67 2007 1027 1041
19. Y. Zhang, and J. Sun Stability of impulsive infinite delay differential equations Appl. Math. Lett. 19 2006 1100 1106
20. Z. Luo, and J. Shen Stability of impulsive functional differential equations via the Liapunov functional Appl. Math. Lett. 22 2009 163 169
21. Z. Luo, and J. Shen Stability and boundedness for impulsive functional differential equations with infinite delays Nonlinear Anal. 46 2001 475 493 (Pubitemid 32888137)
22. X. Li Uniform asymptotic stability and global stability of impulsive infinite delay differential equations Nonlinear Anal. 70 2009 1975 1983
23. V. Lakshmikantham, D. Bainov, and P. Simeonov Theory of Impulsive Differential Equations 1989 World Scientific Singapore
24. D. Bainov, and P. Simeonov Systems with Impulse Effect: Stability Theory and Applications 1989 Chichester Ellis Horwood
25. X. Liu, and K. Rohlf Impulsive control of LotkaVolterra models IMA J. Math. Control Inform. 15 1998 269 284
26. T. Yang, and L. Chua Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication IEEE Trans. Circuits Syst. I 44 1997 976 988 (Pubitemid 127768200)
27. G. Zeng, F. Wang, and J.J. Nieto Complexity of a delayed predatorprey model with impulsive harvest and Holling-type II functional response Adv. Complex Syst. 11 2008 77 97
28. H. Zhang, L. Chen, and J.J. Nieto A delayed epidemic model with stage structure and pulses for management strategy Nonlinear Anal. RWA 9 2008 1714 1726
29. X. Meng Dynamic analysis of MichaelisMenten chemostat-type competition models with time delay and pulse in a polluted environment J. Math. Chem. 47 2010 123 144
30. L. Wang The dynamics of an epidemic model for pest control with impulsive effect Nonlinear Anal. RWA 11 2010 1374 1386
31. S. Haykin Neural Networks 1994 Prentice-Hall NJ
32. S. Niculescu Delay Effects on Stability: A Robust Control Approach 2001 Springer-Verlag New York
33. X. Fu, and X. Li Razumikhin-type theorems on exponential stability of impulsive infinite delay differential systems J. Comput. Appl. Math. 224 2009 1 10
34. A. Weng, and J. Sun Impulsive stabilization of second-order nonlinear delay differential systems Appl. Math. Comput. 214 2009 95 101
35. A. Weng, and J. Sun Impulsive stabilization of second-order delay differential equations Nonlinear Anal. RWA 8 2007 1410 1420
36. X. Li, and P. Weng Impulsive stabilization of two kinds of second-order linear delay differential equations J. Math. Anal. Appl. 291 2004 270 281
37. L. Gimenes, and M. Federson Existence and impulsive stability for second order retarded differential equations Appl. Math. Comput. 177 2006 44 62
38. Z. Luo, and J. Shen Impulsive stabilization of functional differential equations with infinite delays Appl. Math. Lett. 16 2003 695 701