Singular Fractional Continuous-Time and Discrete-Time Linear Systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

New classes of singular fractional continuous-time and discrete-time linear systems are introduced. Electrical circuits are example of singular fractional continuous-time systems. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and Laplace transformation the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional systems if it contains at least one mesh consisting of branches with only ideal supercondensators and voltage sources or at least one node with branches with supercoils. Using the Weierstrass regular pencil decomposition the solution to the state equation of singular fractional discrete-time linear systems is derived. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

fractional; singular; linear circuit; regular pencil; solution; supercondensator; supercoil

PL

ułamkowy; pojedynczy; układ liniowy; pęk regularny; rozwiązanie; superkondensator

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2013
• Tom: Vol. 7, no. 1
• Strony: 26--33
• Opis fizyczny: Bibliogr. 16 poz., wykr.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland,

Bibliografia

• 1. Benvenuti L., Farina L. (2004), A tutorial on the positive realization problem, IEEE Trans. Autom. Control, Vol. 49, No. 5, 651-664.
• 2. Dail L. (1989), Singular control systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin.
• 3. Dodig M. Stosic M. (2009), Singular systems state feedbacks problems, Linear Algebra and its Applications, Vol. 431, No. 8, 1267-1292.
• 4. Fahmy M.H, O’Reill J. (1989), Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment, Int. J. Control, Vol. 49, No. 4, 1421-1431.
• 5. Gantmacher F. R. (1960), The theory of Matrices, Chelsea Publishing Co., New York.
• 6. Kaczorek T. (1992), Linear control systems, Vol. 1, Research Studies Press J. Wiley, New York.
• 7. Kaczorek T. (2004), Infinite eigenvalue assignment by outputfeedbacks for singular systems, Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 1, 19-23.
• 8. Kaczorek T. (2007a), Polynomial and rational matrices. Applications in dynamical systems theory, Springer-Verlag, London.
• 9. Kaczorek T. (2007b), Realization problem for singular positivecontinuous-time systems with delays, Control and Cybernetics, Vol. 36, No. 1, 47-57.
• 10. Kaczorek T. (2008), Fractional positive continuous-time linear systems and their reachability, Int. J. Appl. Math. Comput. Sci., Vol. 18, No. 2, 223-228.
• 11. Kaczorek T. (2010a), Analysis of fractional electrical circuits in transient states, VII Konferencja Naukowo-Techniczna : Logistyka - systemy transportowe - bezpieczeństwo w transporcie, Szczyrk.
• 12. Kaczorek T. (2010b), Positive linear systems with different fractional orders, Bull. Pol. Ac. Sci. Techn., Vol. 58, No. 3, 453-458.
• 13. Kaczorek T. (2011) Selected Problems in Fractional Systems Theory, Springer-Verlag.
• 14. Kucera V. Zagalak P. (1988), Fundamental theorem of state feedback for singular systems, Automatica, Vol. 24, No. 5, 653-658.
• 15. Podlubny I. (1999), Fractional differential equations, Academic Press, New York.
• 16. Van Dooren P. (1979), The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra and Its Applications, Vol. 27, 103-140.