Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Rajagopal Joice Nirmala; Krishnan Balachandran

Kybernetika (2017)

  • Volume: 53, Issue: 1, page 161-178
  • ISSN: 0023-5954

Abstract

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This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.

How to cite

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Joice Nirmala, Rajagopal, and Balachandran, Krishnan. "Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control." Kybernetika 53.1 (2017): 161-178. <http://eudml.org/doc/287937>.

@article{JoiceNirmala2017,
abstract = {This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.},
author = {Joice Nirmala, Rajagopal, Balachandran, Krishnan},
journal = {Kybernetika},
keywords = {fractional delay integrodifferential equation; Laplace transform; controllability; Mittag–Leffler function; Caputo fractional derivative},
language = {eng},
number = {1},
pages = {161-178},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control},
url = {http://eudml.org/doc/287937},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Joice Nirmala, Rajagopal
AU - Balachandran, Krishnan
TI - Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 1
SP - 161
EP - 178
AB - This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.
LA - eng
KW - fractional delay integrodifferential equation; Laplace transform; controllability; Mittag–Leffler function; Caputo fractional derivative
UR - http://eudml.org/doc/287937
ER -

References

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  1. Bagley, R. L., Torvik, P. J., 10.1122/1.549724, J. Rheol. 27 (1983), 201-210. Zbl0515.76012DOI10.1122/1.549724
  2. Bagley, R. L., Torvik, P. J., 10.2514/3.9007, AIAA J. 23 (1985), 918-925. Zbl0562.73071DOI10.2514/3.9007
  3. Balachandran, K., 10.1080/00207178708933892, Int. J. Control. 46 (1987), 193-200. MR0895702DOI10.1080/00207178708933892
  4. Balachandran, K., Dauer, J. P., 10.1109/tac.1987.1104536, IEEE Trans. Autom. Control. 32(1987), 172-174. Zbl0614.93011MR0872593DOI10.1109/tac.1987.1104536
  5. Balachandran, K., Kokila, J., Trujillo, J.J., 10.1016/j.camwa.2012.01.071, Comput. Math. Appl. 64 (2012), 3037-3045. Zbl1268.93021MR2989332DOI10.1016/j.camwa.2012.01.071
  6. Balachandran, K., Zhou, Y., Kokila, J., 10.1016/j.cnsns.2011.12.018, Commun. Nonlinear. Sci. Numer. Simul. 17 (2012), 3508-3520. Zbl1248.93022MR2913988DOI10.1016/j.cnsns.2011.12.018
  7. Balachandran, K., Zhou, Y., Kokila, J., 10.1016/j.camwa.2011.11.061, Comput. Math. Appl. 64(2012), 3201-3209. MR2989348DOI10.1016/j.camwa.2011.11.061
  8. Bellman, R., Cooke, K. L., 10.1002/zamm.19650450612, Academic Press, New York 1963. Zbl0163.10501MR0147745DOI10.1002/zamm.19650450612
  9. Chow, T. S., 10.1016/j.physleta.2005.05.045, Physics Letter A 342 (2005), 148-155. DOI10.1016/j.physleta.2005.05.045
  10. Dauer, J. P., Gahl, R. D., 10.1007/bf00932544, J. Optimiz. Theory. App. 21 (1977), 59-68. Zbl0325.93007MR0433306DOI10.1007/bf00932544
  11. Dauer, J. P., 10.1016/0022-247x(76)90191-8, J. Math. Anal. Appl. 54 (1976), 717-725. Zbl0339.93004MR0415473DOI10.1016/0022-247x(76)90191-8
  12. Halanay, A., 10.1016/s0076-5392(08)x6057-6, Academic Press, New York 1966. Zbl0144.08701MR0216103DOI10.1016/s0076-5392(08)x6057-6
  13. Hale, J., 10.1007/978-1-4612-9892-2, Springer, New York 1977. Zbl0662.34064MR0508721DOI10.1007/978-1-4612-9892-2
  14. He, J. H., 10.1016/s0045-7825(98)00108-x, Comput. Methods. Appl. Mech. Eng. 167 (1998), 57-68. Zbl0942.76077MR1665221DOI10.1016/s0045-7825(98)00108-x
  15. Nirmala, R. Joice, Balachandran, K., 10.5890/dnc.2016.03.007, J. Applied Nonlinear Dynamics 5 (2016), 59-73. MR3577640DOI10.5890/dnc.2016.03.007
  16. Nirmala, R. Joice, Balachandran, K., Germa, L. R., Trujillo, J. J., 10.1016/s0034-4877(16)30007-6, Rep. Math. Phys. 77 (2016), 87-104. MR3461800DOI10.1016/s0034-4877(16)30007-6
  17. Kaczorek, T., 10.1007/978-3-642-20502-6, Springer-Verlag, Berlin 2011. MR2798773DOI10.1007/978-3-642-20502-6
  18. Klamka, J., 10.1080/00207177608932867, Int. J. Control 24(1976), 869-878. MR0424300DOI10.1080/00207177608932867
  19. Klamka, J., 10.1016/0005-1098(76)90046-7, Automatica 12(1976), 633-634. MR0452869DOI10.1016/0005-1098(76)90046-7
  20. Kilbas, A., Srivastava, H. M., Trujillo, J. J., Theory and Application of Fractional Differential Equations., Elsevier, Amsterdam 2006. MR2218073
  21. Machado, J. T., Analysis and design of fractional order digital control systems., Systems Analysis, Modelling and Simulation 27 (1997), 107-122. Zbl0875.93154
  22. Machado, J. T., Costa, A. C., Quelhas, M. D., 10.1016/j.cnsns.2010.11.007, Commun. Nonlinear. Sci. Numer. Simul. 16 (2011), 2963-2969. Zbl1218.92038DOI10.1016/j.cnsns.2010.11.007
  23. Magin, R. L, 10.1615/critrevbiomedeng.v32.i1.10, Critical Rev. Biomed. Eng. 32 (2004), 1-377. DOI10.1615/critrevbiomedeng.v32.i1.10
  24. Mainardi, F., 10.1007/978-3-7091-2664-6_7, In: Fractals and Fractional Calculus in Continuum Mechanics (A. Carpinteri and F. Mainardi, eds.), Springer-Verlag 1997, pp. 291-348. MR1611587DOI10.1007/978-3-7091-2664-6_7
  25. Manzanilla, R., Marmol, L. G., Vanegas, C. J., 10.1155/2010/307409, Abstr. Appl. Anal. 2010 (2010), 1-16. MR2660394DOI10.1155/2010/307409
  26. Miller, K. S., Ross, B., An Introduction to the Fractional Calculus and Fractional Differential Equations., Wiley and Sons, New York 1993. Zbl0789.26002MR1219954
  27. Mur, T., Henriquez, H. R., 10.3934/mcrf.2015.5.845, Math. Control. Relat. F 5(2015), 845-858. Zbl1332.93061MR3485753DOI10.3934/mcrf.2015.5.845
  28. Oguztoreli, M. N., 10.1016/s0076-5392(08)x6192-2, Academic Press, New York 1966. Zbl0143.12101MR0217394DOI10.1016/s0076-5392(08)x6192-2
  29. Oldham, K. B., Spanier, J., 10.1016/s0076-5392(09)x6012-1, Academic Press, New York 1974. MR0361633DOI10.1016/s0076-5392(09)x6012-1
  30. Ortigueira, M. D., 10.1016/s0165-1684(03)00183-x, Signal Process 83 (2003), 2301-2309. Zbl1145.94367DOI10.1016/s0165-1684(03)00183-x
  31. Podlubny, I., Fractional Differential Equations., Academic Press, New York 1999. Zbl1160.65308MR1658022
  32. Podlubny, I., 10.1016/s0076-5392(99)x8001-5, Academic Press, 1999. Zbl0924.34008MR1658022DOI10.1016/s0076-5392(99)x8001-5
  33. Sabatier, J., Agrawal, O. P., (eds.), J. A. Tenreiro-Machado, 10.1007/978-1-4020-6042-7, Springer-Verlag, New York 2007. Zbl1116.00014MR3184154DOI10.1007/978-1-4020-6042-7
  34. Schiff, J. L., 10.1007/978-0-387-22757-3, Springer, New York 1999. Zbl0934.44001MR1716143DOI10.1007/978-0-387-22757-3
  35. Sikora, B., 10.1049/iet-cta.2015.0935, IET Control Theory Appl. 10(2016), 320-327. MR3468656DOI10.1049/iet-cta.2015.0935
  36. Smith, H., 10.1007/978-1-4419-7646-8, Springer, New York 2011. MR2724792DOI10.1007/978-1-4419-7646-8
  37. Wei, J., 10.1016/j.camwa.2012.02.065, Comput. Math. Appl. 64 (2012), 3153-3159. Zbl1268.93027MR2989343DOI10.1016/j.camwa.2012.02.065

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