Positivity of descriptor linear systems with regular pencils

• Autorzy: Kaczorek T.
• Konferencja: Computer Applications in Electrical Engineering 2012 (23-24.04.2012; Poznań, Polska)
• Języki publikacji: EN

Abstrakty

EN

The positivity of descriptor continuous-time and discrete-time linear systems with regular pencils are addressed. Such systems can be reduced to standard linear systems and can be decomposed into dynamical and static parts. Two definitions of the positive systems are proposed. It is shown that the definitions are not equivalent. Conditions for the positivity of the systems and the relationship between two classes of positive systems are established. The considerations are illustrated by examples of electrical circuits and numerical examples.

Słowa kluczowe

EN

descriptor; linear systems; regular pencil

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Poznan University of Technology Academic Journals. Electrical Engineering
• Rocznik: 2012
• Tom: No. 69
• Strony: 9--22
• Opis fizyczny: Bibliogr. 21 poz., rys.

Twórcy

autor

Kaczorek T.

• Białystok University of Technology

Bibliografia

• [1] Dodig M. and Stosic M., “Singular systems state feedbacks problems,” Linear Algebra and its Applications, Vol. 431, No. 8, pp. 1267-1292 (2009).
• [2] Dai L., Singular Control Systems, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin (1989).
• [3] Fahmy M.H., O’Reill J., “Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment,” Int. J. Control, Vol. 49, No. 4, pp. 1421-1431 (1989).
• [4] Gantmacher F.R., The Theory of Matrices, Chelsea Publishing Co., New York (1960).
• [5] Kaczorek T., “Fractional positive continuous-time linear systems and their reachability,” Int. J. Appl. Math. Comput. Sci. Vol. 18, No. 2, pp. 223-228 (2008).
• [6] Kaczorek T., “Infinite eigenvalue assignment by output-feedbacks for singular systems,” Int. J. Appl. Math. Comput. Sci. Vol. 14, No. 1, pp. 19-23 (2004).
• [7] Kaczorek T., Linear Control Systems, Vol. 1, Research Studies Press J. Wiley, New York (1992).
• [8] Kaczorek T., Polynomial and Rational Matrices. Applications in Dynamical Systems Theory, Springer-Verlag, London (2007).
• [9] Kaczorek T., “Positive linear systems with different fractional orders,” Bull. Pol. Ac. Sci. Techn., Vol. 58, No. 3, pp. 453-458 (2010).
• [10] Kaczorek T., “Realization problem for singular positive continuous-time systems with delays”, Control and Cybernetics, Vol. 36, No. 1, pp. 47-57 (2007).
• [11] Kaczorek T., Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin (2011).
• [12] Kaczorek T., “Checking of the positivity of descriptor linear systems by the use of shuffle algorithm”, Archives of Control Sciences (2012).
• [13] Kaczorek T., “Positivity and reachability of fractional electrical circuits”, Acta Mechanica et Automatica, Vol. 3, No. 1, 42-54 (2011).
• [14] Kaczorek T., “Reduction and decomposition of singular fractional discrete-time linear systems,” Acta Mechanica et Automatica, Vol. 5, No. 4 (2011).
• [15] Kaczorek T., “Singular fractional discrete-time linear systems,” Control and Cybernetics, Vol. 40, No. 3 (2011).
• [16] Kaczorek T., “Singular fractional linear systems and electrical circuits,” Int. J. Appl. Math. Comput. Sci., Vol. 21, No. 2, 2011, pp. 379-384.
• [17] Kaczorek T., Positive ID and 2D Systems, Springer-Verlag (2002).
• [18] Kucera V. and Zagalak P., “Fundamental theorem of state feedback for singular systems,” Automatica, Vol. 24, No. 5, pp. 653-658 (1988).
• [19] Luenberger D.G., “Time-invariant descriptor systems,” Automatica, Vol. 14, pp. 473-480 (1978).
• [20] Podlubny I., Fractional Differential Equations, Academic Press, New York (1999).
• [21] Van Dooren P., “The computation of Kronecker’s canonical form of a singular pencil,” Linear Algebra and Its Applications, Vol. 27, pp. 103-140 (1979).