Razumikhin stability theorem for fractional systems with delay

Abstract and Applied Analysis

Volumn 2010, Issue , 2010, Pages

  Baleanu, D ^a,b   Sadati, S J ^c   Ghaderi, R ^c   Ranjbar, A ^c   Abdeljawad Maraaba, T ^a   Jarad, F ^a  

^a CANKAYA UNIVERSITY   (Turkey)

^b INSTITUTE OF SPACE SCIENCES   (Romania)

^c BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77954552119     PISSN: 10853375     EISSN: 16870409     Source Type: Journal    
DOI: 10.1155/2010/124812     Document Type: Article

References (23)

1. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science B.V. xvi+523 North-Holland Mathematics Studies
2. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering
3. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Application 1993 Yverdon, Switzerland Gordon and Breach Science Publishers xxxvi+976
4. West B. J., Bologna M., Grigolini P., Physics of Fractal Operators 2003 New York, NY, USA Springer x+354 Institute for Nonlinear Science
5. Magin R. L., Fractional Calculus in Bioengineering 2006 Connecticut, Mass, USA Begell House Publisher
6. Torvik P. J., Bagley R. L., On the appearance of the fractional derivative in the behavior of real materials Journal of Applied Mechanics, Transactions 1984 51 2 294 298
7. Richard J.-P., Time-delay systems: an overview of some recent advances and open problems Automatica 2003 39 10 1667 1694
8. Chen J., Xu D. M., Shafai B., On sufficient conditions for stability independent of delay IEEE Transactions on Automatic Control 1995 40 9 1675 1680
9. Lee T. N., Dianat S., Stability of time-delay systems IEEE Transactions on Automatic Control 1981 26 4 951 953
10. Weber E., Linear Transient Analysis. Volume II 1956 New York, NY, USA John Wiley Sons xiv+452
11. Jenson V. G., Jeffreys G. V., Mathematical Methods in Chemical Engineering 1977 2nd New York, NY, USA Academic Press
12. Nakagava M., Sorimachi K., Basic characteristics of a fractance device IEICE Transactions, Fundamentals 1992 75 12 1814 1818
13. Lanusse P., Oustaloup A., Mathieu B., Third generation CRONE control 2 Proceedings of the IEEE International Conference on Systems, Man and Cybernetics 1993 149 155
14. Podlubny I., Fractional-order systems and PID -controllers IEEE Transactions on Automatic Control 1999 44 1 208 214
15. Raynaud H.-F., Zerganoh A., State-space representation for fractional order controllers Automatica 2000 36 7 1017 1021
16. Lazarevi M. P., Finite time stability analysis of PD fractional control of robotic time-delay systems Mechanics Research Communications 2006 33 2 269 279
17. Deng W., Li C., L J., Stability analysis of linear fractional differential system with multiple time delays Nonlinear Dynamics 2007 48 4 409 416
18. Merrikh-Bayat F., Karimi-Ghartemani M., An efficient numerical algorithm for stability testing of fractional-delay systems ISA Transactions 2009 48 1 32 37
19. Zhang X., Some results of linear fractional order time-delay system Applied Mathematics and Computation 2008 197 1 407 411
20. Momani S., Hadid S., Lyapunov stability solutions of fractional integrodifferential equations International Journal of Mathematics and Mathematical Sciences 2004 45-48 2503 2507
21. Li Y., Chen Y., Podlubny I., Stability of fractional-order nonlinear dynamic systems: lyapunov direct method and generalized Mittag-Leffler stability Computers and Mathematics with Applications 2010 59 5 1810 1821
22. Hale J. K., Verduyn Lunel S. M., Introduction to Functional-Differential Equations 1993 99 New York, NY, USA Springer x+447 Applied Mathematical Sciences
23. Kequin G., Kharitonov V. L., Chen J., Stability of Time-Delay Systems 2003 Basel, Switzerland Birkhäuser