Asymptotic stability of nonlinear systems with unbounded delays

Journal of Mathematical Analysis and Applications

Volumn 337, Issue 2, 2008, Pages 1010-1021

  Tan, Man Chun ^a  

^a JINAN UNIVERSITY   (China)

Author keywords

Asymptotic stability; Stabilization of time delay system; State feedback control; System with unbounded delay

Indexed keywords

EID: 34548630789     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.04.019     Document Type: Article

References (20)

1. Boyd S., El Ghaoui L., Feron E., and Balakrishnan V. Linear Matrix Inequalities in System and Control Theory (1994), SIAM, Philadelphia, PA
2. Burton T.A. Stability and Periodic Solutions of Ordinary and Functional Differential Equations (2005), Dover Publications Inc., Mineola, NY
3. Burton T.A., and Somolinos A. Asymptotic stability in differential equations with unbounded delay. Electron. J. Qual. Theory Differ. Equ. 13 (1999) 1-19
4. Cermak J. A change of variables in the asymptotic theory of differential equations with unbounded delays. J. Comput. Appl. Math. 143 (2002) 81-93
5. Guan X.P., Chen C.L., Peng H.P., et al. Time-delayed feedback control of time-delay chaotic systems. Internat. J. Bifur. Chaos 13 (2003) 193-205
6. Hale J. Theory of Functional Differential Equations (1977), Springer-Verlag, New York
7. Henríquez H.R., and Hernández E. Stabilization of linear distributed control systems with unbounded delay. J. Math. Anal. Appl. 307 (2005) 321-338
8. Hino Y., Murakami S., and Naito T. Functional Differential Equations with Infinite Delay (1991), Springer-Verlag, New York
9. Iserles A. On the generalized pantograph functional-differential equation. European J. Appl. Math. 4 (1992) 1-38
10. Kharitonov V.L. Robust stability analysis of time delay systems: a survey. Annu. Rev. Control 23 (1999) 185-196
11. Kolmanovskii V., and Myshkis A. Introduction to the Theory and Applications of Functional Differential Equations (1999), Kluwer Academic Publishers, Boston
12. Kolmanovskii V.B., and Nosov V.R. Stability of Functional Differential Equations (1986), Academic Press, Orlando
13. Liu P.-l. Exponential stability for linear time-delay systems with delay dependence. J. Franklin Inst. 340 (2003) 481-488
14. Liu Y. On the θ-method for delay differential equations with infinite lag. J. Comput. Appl. Math. 71 (1996) 177-190
15. Nesterov Y., and Nemirovsky A. Interior Point Polynomial Methods in Convex Programming (1994), SIAM, Philadelphia, PA
16. Tan M. Feedback stabilization of linear systems with proportional delay. Inform. Control 6 (2006) 690-694
17. Wang Q., and Liu X. Exponential stability for impulsive delay differential equations by Razumikhin method. J. Math. Anal. Appl. 309 (2005) 462-473
18. Wang S., and Jia Z. Inequalities in Matrix Theory (1994), Anhui Education Press, Hefei (in Chinese)
19. Xu D.Y. Razumikhin approach in functional differential equations. J. Sichuan Normal Univ. 4 (1995) 41-47
20. Zhang J. Absolute stability analysis in cellular neural networks with variable delays and unbounded delay. Comput. Math. Appl. 47 (2004) 183-194