References

• 1. 1)
     • 14. Kaczorek, T.: ‘Practical stability of positive fractional discrete-time linear systems’, Bull. Pol. Acad. Sci. Tech., 2008, 56, (4), pp. 313–318.
  2. 2)
     • 15. Dzieliński, A., Sierociuk, D., Sarwas, G.: ‘Ultracapacitor parameters identification based on fractional order model’. Proc ECC’09, Budapest, 2009.
  3. 3)
     • 5. Kaczorek, T.: ‘Selected problems of fractional systems theory’ (Springer-Verlag, Berlin, 2012).
  4. 4)
     • 13. Kaczorek, T.: ‘Asymptotic stability of positive fractional 2D linear systems’, Bull. Pol. Acad. Sci. Tech., 2009, 57, (3), pp. 287–292.
  5. 5)
     • 25. Kaczorek, T.: ‘Minimum energy control of fractional positive continuous-time linear systems’. Proc. Conf. MMAR Miedzyzdroje, 26–29 August 2013.
  6. 6)
     • 16. Kaczorek, T.: ‘Reachability and controllability to zero tests for standard and positive fractional discrete-time systems’, J. Eur. Syst. Autom., 2008, 42, (6–8), pp. 769–787.
  7. 7)
     • 2. Kaczorek, T.: ‘Positive 1D and 2D systems’ (Springer-Verlag, London, 2001).
  8. 8)
     • 22. Klamka, J.: ‘Relative controllability and minimum energy control of linear systems with distributed delays in control’, IEEE Trans. Autom. Control, 1976, 21, (4), pp. 594–595 (doi: 10.1109/TAC.1976.1101280).
  9. 9)
     • 19. Vinagre, B.M., Monje, C.A., Calderon, A.J.: ‘Fractional order systems and fractional order control actions’. Lecture 3 IEEE CDC’02 TW#2: Fractional calculus Applications in Automatic Control and Robotics, 2002.
  10. 10)
      • A. Radwan , A. Soliman , A. Elwakil , A. Sedeek . On the stability of linear systems with fractional-order elements. Chaos, Solitons Fractals , 5 , 2317 - 2328
  11. 11)
      • 21. Klamka, J.: ‘Minimum energy control of 2D systems in Hilbert spaces’, Syst. Sci., 1983, 9, (1–2), pp. 33–42.
  12. 12)
      • 3. Kaczorek, T.: ‘Controllability and observability of linear electrical circuits’, Electr. Rev., 2011, 87, (9a), pp. 248–254.
  13. 13)
      • 26. Kaczorek, T.: ‘Minimum energy control of descriptor positive discrete-time linear systems’, COMPEL, 2013, accepted for publication.
  14. 14)
      • 23. Kaczorek, T., Klamka, J.: ‘Minimum energy control of 2D linear systems with variable coefficients’, Int. J. Control, 1986, 44, (3), pp. 645–650 (doi: 10.1080/00207178608933623).
  15. 15)
      • 10. Kaczorek, T.: ‘Positive linear systems consisting of n subsystems with different fractional orders’, IEEE Trans. Circuits Syst., 2011, 58, (6), pp. 1203–1210 (doi: 10.1109/TCSI.2010.2096111).
  16. 16)
      • 6. Oldham, K.B., Spanier, J.: ‘The fractional calculus’ (Academic Press, New York, 1974).
  17. 17)
      • 18. Tenreiro Machado, J.A., Ramiro Barbosa, S.: ‘Functional dynamics in genetic algorithms’, Workshop on Fractional Differenation Appl., 2006, 1, pp. 439–444.
  18. 18)
      • 20. Klamka, J.: ‘Controllability of dynamical systems’ (Kluwer Academic Press, Dordrecht, 1991).
  19. 19)
      • 9. Kaczorek, T.: ‘Fractional positive continuous-time systems and their Reachability’, Int. J. Appl. Math. Comput. Sci., 2008, 18, (2), pp. 223–228 (doi: 10.2478/v10006-008-0020-0).
  20. 20)
      • 11. Busłowicz, M.: ‘Stability of linear continuous time fractional order systems with delays of the retarded type’, Bull. Pol. Acad. Sci. Tech., 2008, 56, (4), pp. 319–324.
  21. 21)
      • 7. Ostalczyk, P.: ‘Epitome of the fractional calculus: theory and its applications in automatics’. Wydawnictwo Politechniki Łódzkiej, Łódź2008(in Polish).
  22. 22)
      • 8. Podlubny, I.: ‘Fractional differential equations’ (Academic Press, San Diego, 1999).
  23. 23)
      • 28. Kaczorek, T.: ‘Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm’, Arch. Control Sci., 2011, 21, (3), pp. 287–298.
  24. 24)
      • 24. Klamka, J.: ‘Controllability and minimum energy control problem of fractional discrete-time systems’, in Baleanu, D., Guvenc, Z.B., Tenreiro Machado, J.A. (Eds.): ‘Chapter in new trends in nanotechology and fractional calculus’ (Springer-Verlag, New York, 2010), pp. 503–509.
  25. 25)
      • 1. Farina, L., Rinaldi, S.: ‘Positive linear systems; theory and applications’ (J. Wiley, New York, 2000).
  26. 26)
      • 4. Kaczorek, T.: ‘Positivity and reachability of fractional electrical circuits’, Acta Mech. Autom., 2011, 3, (1), pp. 42–51.
  27. 27)
      • 12. Dzieliński, A., Sierociuk, D.: ‘Stability of discrete fractional order state-space systems’, J. Vib. Control, 2008, 14, (9/10), pp. 1543–1556 (doi: 10.1177/1077546307087431).
  28. 28)
      • 27. Kaczorek, T.: ‘Linear control systems’ (Research Studies Press and J. Wiley, New York, 1992).