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Minimum energy control of positive time-varying linear systems

Autorzy
Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The minimum energy control problem for the positive time-varying linear systems is formulated and solved. Sufficient conditions for the existence of solution to the problem are established. A procedure for solving of the problem is proposed and illustrated by a numerical example.
Rocznik
Strony
225--228
Opis fizyczny
Bibliogr. 26 poz.
Twórcy
autor
  • Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351 Bialystok, Poland
Bibliografia
  • 1. Busłowicz M. (2008), Stability of linear continuous time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci. Tech., Vol. 56(4), 319-324.
  • 2. Dzieliński A., Sierociuk D. (2008), Stability of discrete fractional order state-space systems, Journal of Vibrations and Control, Vol. 14(9/10), 1543-1556.
  • 3. Dzieliński A., Sierociuk D., Sarwas G. (2009), Ultracapacitor parameters identification based on fractional order model, Proc ECC’09, Budapest.
  • 4. Farina L., Rinaldi S. (2000), Positive Linear Systems; Theory and Applications, J. Wiley, New York.
  • 5. Gantmacher F.R. (1959), The Theory of Matrices, Chelsea, New York.
  • 6. Kaczorek T. (1992), Linear Control Systems, Research Studies Press and J.Wiley, New York.
  • 7. Kaczorek T. (2001a), Externally and internally positive time-varying linear systems, Int. J. Appl. Math. Comput. Sci., Vol. 11(4), 957-964.
  • 8. Kaczorek T. (2001b), Positive 1D and 2D systems, Springer Verlag, London.
  • 9. Kaczorek T. (2008a), Fractional positive continuous-time systems and their Reachability, Int. J. Appl. Math. Comput. Sci., Vol. 18(2), 223-228.
  • 10. Kaczorek T. (2008b), Practical stability of positive fractional discretetime linear systems, Bull. Pol. Acad. Sci. Tech., Vol. 56(4), 313-317.
  • 11. Kaczorek T. (2008c), Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal Européen des Systèmes Automatisés, JESA, Vol. 42(6-8), 769-787.
  • 12. Kaczorek T. (2009), Asymptotic stability of positive fractional 2D linear systems, Bull. Pol. Acad. Sci. Tech., Vol. 57(3), 289-292.
  • 13. Kaczorek T. (2011a), Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm, Archive of Control Sciences, Vol. 21(3), 287-298.
  • 14. Kaczorek T. (2011b), Controllability and observability of linear electrical circuits, Electrical Review, Vol. 87(9a), 248-254.
  • 15. Kaczorek T. (2011c), Positive linear systems consisting of 𝑛 subsystems with different fractional orders, IEEE Trans. Circuits and Systems, Vol. 58(6), 1203-1210.
  • 16. Kaczorek T. (2011d), Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, Vol. 5(2), 42-51.
  • 17. Kaczorek T. (2012), Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
  • 18. Kaczorek T. (2014a), Minimum energy control of descriptor positive discrete-time linear systems, COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, Vol. 33(3), 976 - 988.
  • 19. Kaczorek T. (2014b), Minimum energy control of fractional positive continuous-time linear systems, International Journal of Applied Mathematics and Computer Science, Vol. 24(2), 335-340.
  • 20. Kaczorek T., Klamka J. (1986), Minimum energy control of 2D linear systems with variable coefficients, Int. J. of Control, Vol. 44(3), 645-650.
  • 21. Klamka J. (1976), Relative controllability and minimum energy control of linear systems with distributed delays in control, IEEE Trans. Autom. Contr., Vol. 21(4), 594-595.
  • 22. Klamka J. (1977), Minimum energy control of discrete systems with delays in control, International Journal of Control, Vol. 26(5), 737-744.
  • 23. Klamka J. (1983), Minimum energy control of 2D systems in Hilbert spaces, System Sciences, Vol. 9(1-2), 33-42.
  • 24. Klamka J. (1991), Controllability of Dynamical Systems, Kluwer Academic Press, Dordrecht.
  • 25. Klamka J. (1993), Controllability of dynamical systems-a survey, Archives of Control Sciences, Vol. 2(3-4), 281-307.
  • 26. Klamka J. (2010), Controllability and minimum energy control problem of fractional discrete-time systems, Chapter in “New Trends in Nanotechology and Fractional Calculus”, Eds. Baleanu D., Guvenc Z.B., Tenreiro Machado J.A., Springer-Verlag, New York, 503-509.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-80523349-9ea7-4c8e-a716-aa3749cf9fa2
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