Have a personal or library account? Click to login
Controllability of nonlinear stochastic systems with multiple time-varying delays in control Cover

Controllability of nonlinear stochastic systems with multiple time-varying delays in control

Open Access
|Jun 2015

References

  1. Balachandran, K. (1987). Global relative controllability of nonlinear systems with time-varying multiple delays in control, International Journal of Control 46(1): 193-200.10.1080/00207178708933892
  2. Balachandran, K. and Dauer, J.P. (1996). Null controllability of nonlinear infinite delay systems with time varying multiple delays in control, Applied Mathematics Letters 9(3): 115-121.10.1016/0893-9659(96)00042-0
  3. Balachandran, K., and Karthikeyan, S. (2009). Controllability of stochastic systems with distributed delays in control, International Journal of Control 82(7): 1288-1296.10.1080/00207170802549537
  4. Balachandran, K., Kokila, J. and Trujillo, J.J. (2012). Relative controllability of fractional dynamical systems with multiple delays in control, Computers & Mathematics with Applications 64(10): 3037-3045.10.1016/j.camwa.2012.01.071
  5. Basin, M., Rodriguez-Gonzaleza, J. and Martinez-Zunigab, M. (2004). Optimal control for linear systems with time delay in control input, Journal of the Franklin Institute 341(1): 267-278.10.1016/j.jfranklin.2003.12.004
  6. Dauer, J.P., Balachandran, K. and Anthoni, S.M. (1998). Null controllability of nonlinear infinite neutral systems with delays in control, Computers & Mathematics with Applications 36(1): 39-50.10.1016/S0898-1221(98)00115-1
  7. Enrhardt, M. and W. Kliemann, W. (1982). Controllability of stochastic linear systems, Systems and Control Letters 2(3): 145-153.10.1016/0167-6911(82)90012-3
  8. Gu, K. and Niculescu, S.I. (2003). Survey on recent results in the stability and control of time-delay systems, ASME Transactions: Journal of Dynamic Systems, Measurement, and Control 125(2): 158-165.10.1115/1.1569950
  9. Guendouzi, T. and Hamada, I. (2013). Relative controllability of fractional stochastic dynamical systems with multiple delays in control, Malaya Journal of Matematik 1(1): 86-97.
  10. Guendouzi, T. and Hamada, I. (2014). Global relative controllability of fractional stochastic dynamical systems with distributed delays in control, Sociedade Paranaense de Matematica Boletin 32(2): 55-71.10.5269/bspm.v32i2.20583
  11. Karthikeyan, S. and Balachandran, K. (2013). On controllability for a class of stochastic impulsive systems with delays in control, International Journal of Systems Science 44(1): 67-76.10.1080/00207721.2011.581394
  12. Klamka, J. (1976). Controllability of linear systems with time-variable delays in control, International Journal of Control 24(2): 869-878.10.1080/00207177608932867
  13. Klamka, J. (1978). Relative controllability of nonlinear systems with distributed delays in control, International Journal of Control 28(2): 307-312.10.1080/00207177808922456
  14. Klamka, J. (1980). Controllability of nonlinear systems with distributed delay in control, International Journal of Control 31(1): 811-819.10.1080/00207178008961084
  15. Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht.
  16. Klamka, J. (2000). Schauder’s fixed point theorem in nonlinear controllability problems, Control and Cybernetics 29(2): 153-165.
  17. Klamka, J. (2007a). Stochastic controllability of linear systems with delay in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(1): 23-29.
  18. Klamka, J. (2007b). Stochastic controllability of linear systems with state delays, International Journal of Applied Mathematics and Computer Science 17(1): 5-13, DOI: 10.2478/v10006-007-0001-8.10.2478/v10006-007-0001-8
  19. Klamka, J. (2008a). Stochastic controllability of systems with variable delay in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(3): 279-284.
  20. Klamka, J. (2008b). Stochastic controllability and minimum energy control of systems with multiple delays in control, Applied Mathematics and Computation 206(2): 704-715.10.1016/j.amc.2008.08.059
  21. Klamka, J. (2009). Constrained controllability of semilinear systems with delays, Nonlinear Dynamics 56(4): 169-177.10.1007/s11071-008-9389-4
  22. Klamka, J. (2013), Controllability of dynamical systems. A survey, Bulletin of the Polish Academy of Sciences: Technical Sciences 61(2): 335-342.10.2478/bpasts-2013-0031
  23. Klein, E.J. and Ramirez, W.F. (2001). State controllability and optimal regulator control of time-delayed systems, International Journal of Control 74(3): 281-89.10.1080/00207170010003469
  24. Li, W. (1970). Mathematical Models in the Biological Sciences, Master’s thesis, Brown University, Providence, RI.
  25. Mahmudov, N.I. (2001). Controllability of linear stochastic systems, IEEE Transactions on Automatic Control 46(1): 724-731.10.1109/9.920790
  26. Mahmudov, N.I., and Denker, A. (2000). On controllability of linear stochastic systems, International Journal of Control 73(2): 144-151.10.1080/002071700219849
  27. Mahmudov, N.I., and Zorlu, S. (2003). Controllability of nonlinear stochastic systems, International Journal of Control 76(2): 95-104.10.1080/0020717031000065648
  28. Oksendal, B. (2003). Stochastic Differential Equations. An Introduction with Applications, Sixth Edition, Springer-Verlag, Berlin.
  29. Richard, J.P. (2003). Time-delay systems: An overview of some recent advances and open problems, Automatica 39(10): 1667-1694.10.1016/S0005-1098(03)00167-5
  30. Somasundaram, D. and Balachandran, K. (1984). Controllability of nonlinear systems consisting of a bilinear mode with distributed delays in control, IEEE Transactions on Automatic Control AC-29(2): 573-575.10.1109/TAC.1984.1103583
  31. Shen, L., and Sun, J. (2012). Relative controllability of stochastic nonlinear systems with delay in control, Nonlinear Analysis: Real World Applications 13(1): 2880-2887.10.1016/j.nonrwa.2012.04.017
  32. Sikora, B. and Klamka, J. (2012). On constrained stochastic controllability of dynamical systems with multiple delays in control, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(2): 301-305.10.2478/v10175-012-0040-7
  33. Zhang, R., Li, T., and Guo, L. (2013). H∞ control for flexible spacecraft with time-varying input delay, Mathematical Problems in Engineering 23: 1-6. Zabczyk, J. (1981). Controllability of stochastic linear systems, Systems & Control Letters 1(1): 25-31.
DOI: https://doi.org/10.1515/amcs-2015-0015 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 207 - 215
Submitted on: Jan 17, 2014
Published on: Jun 25, 2015
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2015 Shanmugasundaram Karthikeyan, Krishnan Balachandran, Murugesan Sathya, published by University of Zielona Góra
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.