Analysis of pointwise completeness and pointwise degeneracy of positive fractional descriptor electrical circuits by the use of Drazin inverse of matrices

• Autorzy: Kaczorek, T.

Warianty tytułu

EN

Analiza punktowej zupełności i punktowej degeneracji dodatnich deskryptowych obwodów elektrycznych rzędu niecałkowitego przy użyciu odwrotności Drazina macierzy

• Języki publikacji: EN

Abstrakty

EN

It is shown that every positive fractional descriptor electrical circuit is a descriptor linear system with regular pencil. The pointwise completeness and pointwise degeneracy of these electrical circuits are analyzed by the use of the method based on Drazin inverse of matrices. Conditions for the pointwise completeness and pointwise degeneracy of the electrical circuits are established and illustrated by an example.

PL

W pracy pokazano, że każdy dodatni deskryptowy obwód elektryczny rzędu niecałkowitego jest układem liniowym o pęku regularnym. Punktowa zupełność i punktowa degeneracja tej klasy układów przeanalizowano przy użyciu odwrotności Drazina macierzy tych obwodów. Podano warunki punktowej zupełności i punktowej degeneracji tej klasy obwodów elektrycznych. Rozważania ogólne zostały zilustrowane przykładem dodatniego obwodu deskryptowego rzędu niecałkowitego.

Słowa kluczowe

PL

obwód elektryczny; punktowa zupełność; punktowa degeneracja; odwrotność Drazina

EN

electrical circuit; point completeness; point degeneration; inverse Drazina

• Czasopismo: Logistyka
• Rocznik: 2014
• Tom: nr 3
• Strony: 2669--2677
• Opis fizyczny: Bibliogr. 28 poz., rys., pełen tekst na CD

Twórcy

autor

Kaczorek, T.

• Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok,

Bibliografia

• 1. Bru, R., Coll, C., Romero-Vivo S. and Sanchez, E. (2003), “Some problems about structural properties of positive descriptor systems”, Lecture Notes in Control and Inform. Sci., vol. 294, Springer, Berlin, 233-240.
• 2. Bru, R., Coll, C. and Sanchez, E. (2002), “Structural properties of positive linear time-invariant difference-algebraic equations”, Linear Algebra Appl., vol. 349, 1-10.
• 3. Busłowicz M., Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order. Zesz. Nauk. Pol. Śląskiej, Automatyka, No. 151, 2008, pp. 19-24 (in Polish).
• 4. Busłowicz M., Kociszewski R., Trzasko W., Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays. Zesz. Nauk. Pol. Śląskiej, Automatyka, No. 145, 2006, pp. 55-56 (in Polish).
• 5. Choundhury A. K., Necessary and sufficient conditions of pointwise completeness of linear timeinvariant delay-differential systems. Int. J. Control, Vol. 16, No. 6, 1972, pp. 1083-1100.
• 6. Campbell, S.L., Meyer, C.D. and Rose, N.J. (1976), “Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients”, SIAMJ Appl. Math., vol. 31, no. 3, 411-425.
• 7. Dai, L. (1989), “Singular control systems”, Lectures Notes in Control and Information Sciences, Springer-Verlag, Berlin.
• 8. Guang-Ren Duan, Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
• 9. L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York 2000.
• 10.Kaczorek T., Busłowicz M., Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems, Journal of Automation, Mobile Robotics & Intelligent Systems, Vol. 3, No. 1, 2009, pp.8-11.
• 11.Kaczorek, T. (2013), “Application of Drazin inverse to analysis of descriptor fractional discretetime linear systems with regular pencils”, Int. J. Appl. Math. Comput. Sci., vol. 23, no. 1, 29-34.
• 12.Kaczorek, T. (2011a), “Checking of the positivity of descriptor linear systems by the use of the shuffle algorithm”, Archives of Control Sciences, vol. 21, no. 3, 2011, 287-298.
• 13.Kaczorek T., Drazin inverse matrix method for fractional descriptor continuous-time linear systems, Submitted to Bull. Pol. Ac. Techn. Sci., 2013.
• 14.Kaczorek, T. (2004), “Infinite eigenvalue assignment by output-feedbacks for singular systems”, Int. J. Appl. Math. Comput. Sci., vol. 14, no. 1, 19-23.
• 15.Kaczorek, T. (1992), Linear Control Systems, vol. 1, Research Studies Press J. Wiley, New York.
• 16.Kaczorek, T. (2013), “Minimum energy control of positive fractional descriptor continuous-time linear systems”, IET Control Theory and Applications (in Press).
• 17.Kaczorek T., Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models, COMPEL, vol. 30, no. 2, 2011, 656-670.
• 18.Kaczorek T., Pointwise completeness and pointwise degeneracy of standard and positive fractional linear systems with state-feedbacks, Archives of Control Sciences, Vol. 19, 2009, pp.295-306.
• 19.Kaczorek T., Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks, JAMRIS, Vol. 4, No. 1, 2010, pp. 3-7.
• 20.Kaczorek, T. (2002), Positive 1D and 2D Systems, Springer-Verlag, London.
• 21.Kaczorek T. (2011), “Reduction and decomposition of singular fractional discrete-time linear systems”, Acta Mechanica et Automatica, Vol. 5, No. 4, 2011, 62-66.
• 22.Kaczorek, T. (2011b), Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin.
• 23.Kaczorek T. (2011), “Singular fractional discrete-time linear systems”, Control and Cybernetics, vol. 40, no.3, 753-761.
• 24.Olbrot A., On degeneracy and related problems for linear constant time-lag systems, Ricerche di Automatica, Vol. 3, No. 3, 1972, pp.203-220.
• 25. Popov V. M., Pointwise degeneracy of linear time-invariant delay-differential equations, Journal of Diff. Equation, Vol. 11, 1972, pp.541-561.
• 26. Trzasko W., Busłowicz M., Kaczorek T., Pointwise completeness of discrete-time cone-systems with delays, Proc. EUROCON 2007, Warsaw, pp. 606-611.
• 27.Weiss L., Controllability for various linear and nonlinear systems models, Lecture Notes in Mathematics, Vol. 144, Seminar on Differential Equations and Dynamic System II, Springer, Berlin 1970, pp. 250-262.
• 28.Virnik E.: Stability analysis of positive descriptor systems, Linear Algebra and its Applications, vol. 429, 2008, pp. 2640-2659.