References

• 1. 1)
     • 26. Balachandran, K., Dauer, J.P.: ‘Controllability of nonlinear systems in Banach spaces: a survey’, J. Optim. Theory Appl., 2002, 115, (1), pp. 7–28 (doi: 10.1023/A:1019668728098).
  2. 2)
     • 9. Matignon, D.: ‘Stability Properties for generalized fractional differential systems’, ESAIM Proc., 1998, 5, pp. 145–158 (doi: 10.1051/proc:1998004).
  3. 3)
     • 40. Kaczorek, T.: ‘Selected problems of fractional systems theory’ (Springer-Verlag, Berlin, 2011).
  4. 4)
     • 28. Renardy, M.: ‘On control of shear flow of an upper convected Maxwell fluid’, ZAMM-Z Angew. Math. Mech., 2007, 87, (3), pp. 213–218 (doi: 10.1002/zamm.200610313).
  5. 5)
     • 19. Chen, Y.Q., Ahn, H.S., Xue, D.: ‘Robust controllability of interval fractional order linear time invariant systems’, Signal Process., 2006, 86, (10), pp. 2794–2802 (doi: 10.1016/j.sigpro.2006.02.021).
  6. 6)
     • 18. Das, S.: Functional fractional calculus for system identification and controls (Springer-Verlag, Berlin, 2008).
  7. 7)
     • 13. Lanusse, P., Poinot, T., Cois, O.: ‘Tuning of an active suspension system using a fractional controller and a closed-loop tuning’. Proc. 11th Int. Conf. Advanced Robotics, Coimbra, Portugal, 2003, pp. 258–263.
  8. 8)
     • 27. Klamka, J.: ‘Schauder's fixed-point theorem in nonlinear controllability problems’, Control Cybern., 2000, 29, (1), pp. 153–165.
  9. 9)
     • 22. Balachandran, K., Park, J.Y., Trujillo, J.J.: ‘Controllability of nonlinear fractional dynamical systems’, Nonlinear Anal. Theory Methods Appl., 2012, 75, (4), pp. 1919–1926 (doi: 10.1016/j.na.2011.09.042).
  10. 10)
      • 17. Petráŝ, I., Vinagre, B.M.: ‘Practical application of digital fractional-order controller to temperature control’, Acta Montan. Slovaca, 2002, 7, (2), pp. 131–137.
  11. 11)
      • 1. Magin, R.L.: ‘Fractional calculus models of complex dynamics in biological tissues’, Comput. Math. Appl., 2010, 59, (5), pp. 1586–1593 (doi: 10.1016/j.camwa.2009.08.039).
  12. 12)
      • 39. Chikrii, A.A., Matichin, I.I.: ‘Presentation of solutions of linear systems with fractional derivatives in the sense of Riemann–Liouville, Caputo and Miller-Ross’, J. Autom. Inf. Sci., 2008, 40, (6), pp. 1–11 (doi: 10.1615/JAutomatInfScien.v40.i6.10).
  13. 13)
      • 15. Fonseca, N.M., Tenreiro, J.A.: ‘Fractional-order hybrid control of robotic manipulators’. Proc. 11th Int. Conf. Advanced Robotics, (Coimbra, Portugal, 2003), pp. 393–398.
  14. 14)
      • 10. Oustaloup, A., Sabatier, J., Lanusse, P., Malti, R., Melchior, P., Moreau, X., Moze, M.: ‘An overview of the CRONE approach in system analysis, modeling and identification, observation and control’. Proc. 17th IFAC World Congress, Seoul, Korea, July 2008, pp. 14254–14265.
  15. 15)
      • 20. Klamka, J.: ‘Controllability and minimum energy control problem of fractional discrete time systems’, in Baleanu, D., Guvenc, Z.B., Machado, J.A.T. (Eds.): ‘New trends in nanotechnology and fractional calculus’ (Springer-Verlag, New York, 2010), pp. 503–509.
  16. 16)
      • 32. Klamka, J.: ‘Constrained controllability of semilinear systems’, Nonlinear Anal. Theory Methods Appl., 2001, 47, (5), pp. 2939–2949 (doi: 10.1016/S0362-546X(01)00415-1).
  17. 17)
      • 34. Anichini, G.: ‘Global controllability of nonlinear control processes with prescribed controls’, J. Optim. Theory Appl., 1980, 32, (2), pp. 183–199 (doi: 10.1007/BF00934723).
  18. 18)
      • 3. Le Mehaute, A., Crepy, G.: ‘Introduction to transfer and motion in fractal media: the geometry of kinetics’, Solid State Ion., 1983, 9–10, (1), pp. 17–30 (doi: 10.1016/0167-2738(83)90207-2).
  19. 19)
      • 12. Calderoń, A.J., Vinagre, B.M., Feliu, V.: ‘Linear fractional order control of a DC–DC buck converter’. Proc. European Control Conf., Cambridge, UK, 2003.
  20. 20)
      • 29. Klamka, J.: ‘Constrained controllability of nonlinear systems’, J Math. Anal. Appl., 1996, 201, (2), pp. 365–374 (doi: 10.1006/jmaa.1996.0260).
  21. 21)
      • 7. Manabe, S.: ‘The non integer integral and its application to control systems’, ETJ Japan, 1961, 6, (3–4), pp. 83–87.
  22. 22)
      • 5. Miller, K.S., Ross, B.: ‘An introduction to the fractional calculus and fractional differential equations’ (Wiley, New York, 1993).
  23. 23)
      • 11. Valerio, D., Sa da Costa, J.: ‘Introduction to single-input, single-output fractional control’, IET Control Theory Appl., 2011, 5, (8), pp. 1033–1057 (doi: 10.1049/iet-cta.2010.0332).
  24. 24)
      • 24. Balachandran, K., Zhou, Y., Kokila, J.: ‘Relative controllability of fractional dynamical systems with time varying delays in control’, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, (9), pp. 3508–3520 (doi: 10.1016/j.cnsns.2011.12.018).
  25. 25)
      • 14. Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D., Feliu, V.: ‘Fractional-order systems and controls; fundamentals and applications’ (Springer, London, 2010).
  26. 26)
      • 30. Klamka, J.: ‘Constrained controllability of dynamical systems’, Int. J. Appl. Math. Comput. Sci., 1999, 9, (9), pp. 231–244.
  27. 27)
      • 38. Kexue, L., Jigen, P.: ‘Laplace transform and fractional differential equations’, Appl. Math. Lett., 2011, 24, (12), pp. 2019–2023 (doi: 10.1016/j.aml.2011.05.035).
  28. 28)
      • 6. Podlubny, I.: ‘Fractional differential equations: an introduction to fractional derivatives, fractional differential equations to methods of their solution and some of their applications’ (Academic Press, 1999).
  29. 29)
      • 37. Karthikeyan, S., Balachandran, K.: ‘Constrained controllability of nonlinear stochastic impulsive systems’, Int. J. Appl. Math. Comput. Sci., 2011, 21, (2), pp. 307–316 (doi: 10.2478/v10006-011-0023-0).
  30. 30)
      • 16. Monje, C.A., Ramos, F., Feliu, V., Vinagre, B.M.: ‘Tip position control of a lightweight flexible manipulator using a fractional order controller’, IEE Proc. D, Control Theory Appl., 2007, 1, (5), pp. 1451–1460 (doi: 10.1049/iet-cta:20060477).
  31. 31)
      • 31. Klamka, J.: ‘Constrained approximate controllability’, IEEE Trans. Autom. Control, 2000, 45, (9), pp. 1745–1749 (doi: 10.1109/9.880640).
  32. 32)
      • 2. West, B.J., Bologna, M., Grigolini, P.: ‘Physics of fractal operators’ (Springer-Verlag, Berlin, 2003).
  33. 33)
      • 33. Lukes, D.L.: ‘Global controllability of nonlinear systems’, SIAM J. Control Optim., 1972, 10, (1), pp. 112–126 (doi: 10.1137/0310011).
  34. 34)
      • 21. Balachandran, K., Kokila, J.: ‘On the controllability of fractional dynamical systems’, Int. J. Appl. Math. Comput. Sci., 2012, 22, (3), pp. 523–531.
  35. 35)
      • 8. Chen, Y.Q., Petráŝ, I., Xue, D.: ‘Fractional order control – a tutorial.’ American Control Conf., 2009, pp. 1397–1411.
  36. 36)
      • 35. Anichini, G.: ‘Controllability and controllability with prescribed controls’, J. Optim. Theory Appl., 1983, 39, (1), pp. 35–45 (doi: 10.1007/BF00934603).
  37. 37)
      • 25. Balachandran, K., Dauer, J.P.: ‘Controllability of nonlinear systems via fixed point theorems’, J. Optim. Theory Appl., 1987, 53, (3), pp. 345–352 (doi: 10.1007/BF00938943).
  38. 38)
      • 4. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: ‘Theory and applications of fractional differential equations’ (Elsevier, Amsterdam, 2006).
  39. 39)
      • 23. Balachandran, K., Zhou, Y., Kokila, J.: ‘Relative controllability of fractional dynamical systems with distributed delays in control’, Comput. Math. Appl., 2012, 64, (10), pp. 3201–3209 (doi: 10.1016/j.camwa.2011.11.061).
  40. 40)
      • 36. Balachandran, K., Karthikeyan, S.: ‘Controllability of nonlinear stochastic systems with prescribed controls’, IMA J. Math. Control Inf., 2010, 27, (1), pp. 77–89 (doi: 10.1093/imamci/dnq002).