On asymptotic stability of delay-difference systems

Applied Mathematics and Computation

Volumn 176, Issue 2, 2006, Pages 759-767

  Liao, Xin Yuan ^a,b   Zhu, Hui Yan ^b   Chen, Feng de ^c  

^a SHANGHAI UNIVERSITY   (China)

^b UNIVERSITY OF SOUTH CHINA   (China)

^c FUZHOU UNIVERSITY   (China)

Author keywords

Asymptotic stability; Delay difference equations; Lyapunov function; Matrix inequalities; Stability criteria

Indexed keywords

ASYMPTOTIC STABILITY; DIFFERENTIAL EQUATIONS; STABILITY CRITERIA;

DELAY-DIFFERENCE EQUATIONS; LYAPUNOV FUNCTION; MATRIX INEQUALITIES;

SYSTEM STABILITY;

EID: 33646361561     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.10.023     Document Type: Article

References (21)

1. Cahlon B. On stability of a first-order complex delay differential equation. Nonlinear Anal.: Read Word Appl. 3 3 (2002) 413-429
2. Cao D.Q., and He P. Stability criteria of linear neutral systems with a single delay. Appl. Math. Comput. 148 (2004) 135-143
3. Han Q.L. On delay-dependent stability for neutral delay-differential systems. Int. J. Appl. Math. Comput. Sci. 11 4 (2001) 965-976
4. Hu G.D., Hu G.D., and Zou X.F. Stability of linear neutral systems with multiple delays: boundary criteria. Appl. Math. Comput. 148 (2004) 707-715
5. X.Y. Liao, W.T. Li, Y.N. Raffoul, Boundedness in nonlinear functional difference equations via non-negative definite Lyapunov functionals with applications to Volterra discrete systems, J. Nonlinear, in press.
6. Elaydi S. An Introduction to Difference Equations. second ed. (1999), Springer-Verlag, New York
7. Eloe P., Islam M., and Raffoul Y.N. Uniform asymptotic stability in nonlinear Volterra discrete systems. Comput. Math. Appl. 45 6-9 (2003) 1033-1039
8. X.Y. Liao, S.S. Cheng, Convergent and divergent solutions of a discrete nonautonomous Lotka-Volterra Model, Tamkang J. Math. (in press).
9. Li W.T., and Raffoul Y.N. Classification and existence of positive solutions of systems of Volterra nonlinear difference equations. Appl. Math. Comput. 155 2 (2004) 469-478
10. Islam M., and Raffoul Y.N. Uniform asymptotic stability in linear Volterra difference equations. Panamer. Math. J. 11 1 (2001) 61-73
11. Islam M., and Raffoul Y.N. Exponential stability in nonlinear difference equations. J. Differen. Equat. Appl. 9 9 (2003) 819-825
12. X.Y. Liao, W.T. Li, Y.N. Raffoul, Asymptotic behavior of solutions of a class of nonlinear difference systems, Adv. Difference Equat. (in review).
13. Medina R. Asymptotic behavior of Volterra difference equations. Comput. Math. Appl. 41 5-6 (2001) 679-687
14. Medina R. The asymptotic behavior of the solutions of a Volterra difference equation. Comput. Math. Appl. 181 (1994) 19-26
15. X.Y. Liao, Z.G. Ouyang, On a delay population dynamical systems of difference equations (in review).
16. Raffoul Y.N., and Dib Y. Boundedness and stability in nonlinear discrete systems with nonlinear perturbation. J. Differen. Equat. Appl. 9 (2003) 853-862
17. Boyd S., Ghaoui L.E., Feron E., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia
18. Raffoul Y.N. General theorems for stability and boundedness for nonlinear functional discrete systems. J. Math. Anal. Appl. 279 (2003) 639-650
19. K. Gu, An integral inequality in the stability problem of time-delay systems, in: Proc. 39th IEEE CDC Conf., Sydney, Australia, 2000, pp. 2805-2810.
20. Song Y., and Baker C.T.H. Linearized stability analysis of discrete Volterra equations. J. Math. Anal. Appl. 294 (2004) 310-333
21. Hale J.K., and Lunel S.M.V. Introduction to Functional Differential Equations (1993), Springer-Verlag, New York