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Eigenvalue assignment in fractional descriptor discrete-time linear systems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of eigenvalue assignment in fractional descriptor discrete-time linear systems is considered. Necessary and sufficient conditions for the existence of a solution to the problem are established. A procedure for computation of the gain matrices is given and illustrated by a numerical example.
Rocznik
Strony
119--128
Opis fizyczny
Bibliogr. 31 poz., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok, Poland
autor
  • Białystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
  • [1] R. Bru, C. Coll and E. Sanchez: About positively discrete-time singular systems. In Mastorakis M.E. (Ed.), System and Control: Theory and Applications, World Scientific and Engineering Society, Athens, 2000, 44-48.
  • [2] R. Bru, C. Coll, S. Romero-Vivo and E. Sanchez: Some problems about structural properties of positive descriptor systems. In Benvenuti A., de Santis A. and Farina L. (Eds.), Positive Systems, Lecture Notes in Control and Information Sciences, 294 (2003), Springer, Berlin, 233-240.
  • [3] A. Bunse-Gerstner , N. Nichols and V. Mehrmann: Regularization of descriptor systems by derivative and proportional state feedback. SIAM J. on Matrix Analysis and Applications, 13(1), (1992), 46-67.
  • [4] S. L. Campbell, C. D. Meyer and N. J. Rose: Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAM J. on Applied Mathematics, 31(3), (1976), 411-425.
  • [5] L. Dai: Singular Control Systems. Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1989.
  • [6] M. Dodig and M. Stosic: Singular systems state feedbacks problems. Linear Algebra and its Applications, 431(8), (2009), 1267-1292.
  • [7] G. R. Duan: Analysis and Design of Descriptor Linear Systems. Springer, New York, 2010.
  • [8] A. Dzieliński, D. Sierociuk and G. Sarwas: Ultracapacitor parameters identification based on fractional order model. Proc. 10th European Control Conference ECC’09, Budapest, (2009).
  • [9] M. M. Fahmy and J. O’Reill: Matrix pencil of closed-loop descriptor systems: Infinite-eigenvalues assignment. Int. J. of Control, 49(4), (1989), 1421-1431.
  • [10] T. Kaczorek: Descriptor positive discrete-time and continuous-time nonlinear systems. Proc. of SPIE, 9290(2014), 1-11.
  • [11] T. Kaczorek: Linear Control Systems vol. 1, Research Studies Press, J. Wiley, New York, 1992.
  • [12] T. Kaczorek: New stability tests of positive standard and fractional linear systems. Circuits and Systems, 2(4), (2011), 261-268.
  • [13] T. Kaczorek: Positive 1D and 2D Systems, Springer-Verlag, London, 2001.
  • [14] T. Kaczorek: Positivity and linearization of a class of nonlinear discrete-time systems by state feedbacks. Logistyka, 6 (2014), 5078-5083.
  • [15] T. Kaczorek: Positive descriptor discrete-time linear systems. Problems of Nonlinear Analysis in Engineering Systems, 1(7), (1998), 38-54.
  • [16] T. Kaczorek: Positivity and stability of discrete-time nonlinear systems. Proc. of 2nd IEEE Intern. Conf. on Cybernetics CYBCONF, (2015), Gdynia, Poland.
  • [17] T. Kaczorek: Positive singular discrete time linear systems. Bull. Pol. Acad. Techn. Sci., 45(4), (1997), 619-631.
  • [18] T. Kaczorek: Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin 2012.
  • [19] T. Kaczorek: Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa, 1998 (in Polish).
  • [20] T. Kaczmarek and K. Rogowski: Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, 13 Springer, 2015.
  • [21] J. Klamka: Controllability of dynamical systems. A survey. Bull. Pol. Acad. Techn. Sci., 61(2), (2013), 221-229.
  • [22] Kucera and P. Zagalak: Fundamental theorem of state feedback for singular systems. Automatica, 24(5), (1988), 653-658.
  • [23] K. B. Oldham and J. Spanier: The Fractional Calculus. Academic Press, New York 1974.
  • [24] P. Ostalczyk: Discrete Fractional Calculus. World Scientific Publ. Co., New Jersey 2016.
  • [25] P. Ostalczyk: Epitome of the fractional calculus: Theory and its Applications in Automatics. Wydawnictwo Politechniki Łódzkiej, Łód´z, 2008 (in Polish).
  • [26] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego 1999.
  • [27] A. G. Radwan, A. M. Soliman, A. S. Elwakil and A. Sedeek: On the stability of linear systems with fractional-order elements. Chaos, Solitons and Fractals, 40(5), (2009), 2317-2328.
  • [28] E. J. Solteiro Pires, J. A. Tenreiro Machado and P. B. Moura Oliveira: Fractional dynamics in genetic algorithms. Workshop on Fractional Differentiation and its Application, 2 (2006), 414-419.
  • [29] P. Van Dooren: The computation of Kronecker’s canonical form of a singular pencil. Linear Algebra and its Applications, 27 (1979), 103-140.
  • [30] B. M. Vinagre, C. A. Monje and A. J. Calderon: Fractional order systems and fractional order control actions. Lecture 3 IEEE CDC’02 TW#2: Fractional calculus Applications in Automatic Control and Robotics, (2002).
  • [31] E. Virnik: Stability analysis of positive descriptor systems. Linear Algebra and its Applications, 429(10), (2008), 2640-2659.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
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