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Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.
Rocznik
Strony
177--187
Opis fizyczny
Bibliogr. 30 poz., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok
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] 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.
  • [4] L. Dai: Singular Control Systems. Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, 1989.
  • [5] M. Dodig and M. Stosic: Singular systems state feedbacks problems. Linear Algebra and its Applications, 431(8), (2009), 1267-1292.
  • [6] G. R. Duan: Analysis and Design of Descriptor Linear Systems, Springer, New York, 2010.
  • [7] 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.
  • [8] L. Farina and S. Rinaldi: Positive Linear Systems; Theory and Applications. J. Wiley, New York, 2000.
  • [9] F. R. Gantmacher: The Theory of Matrices. Chelsea Pub. Comp., London, 1959.
  • [10] T. Kaczorek: An extension of Klamka’s method of minimum energy control to fractional positive discrete-time linear systems with bounded inputs. Bulletin of the Polish Academy of Sciences - Technical Sciences, 62(2), (2014), 227-231.
  • [11] T. Kaczorek: Descriptor positive discrete-time and continuous-time nonlinear systems. Proc. of SPIE, 9290 2014, 1-11.
  • [12] T. Kaczorek.: Linear Control Systems, vol. 1, Research Studies Press. J. Wiley, New York, 1992.
  • [13] T. Kaczorek: Minimum energy control of descriptor positive discrete-time linear systems. COMPEL, 33(3), (2014), 976-988.
  • [14] T. Kaczorek: Minimum energy control of fractional positive continuous-time linear systems. Bulletin of the Polish Academy of Sciences - Technical Sciences, 61(4), (2013), 803-807.
  • [15] T. Kaczorek: Minimum energy control of fractional positive discrete-time linear systems with bounded inputs. Archives of Control Sciences, 23(2), (2013), 205-211.
  • [16] T. Kaczorek: Minimum energy control of positive electrical circuits. Proc. of 19th Int. Conf. of Methods and Models in Automation and Robotics, 2-5 September, (2014), Miedzyzdroje, Poland.
  • [17] T. Kaczorek: Positive 1D and 2D Systems. Springer-Verlag, London, 2001.
  • [18] T. Kaczorek: Positivity and linearization of a class of nonlinear discrete-time systems by state feedbacks. Logistyka, 6 (2014), 5078-5083.
  • [19] T. Kaczorek: Positive descriptor discrete-time linear systems. Problems of Nonlinear Analysis in Engineering Systems, 1(7), (1998), 38-54.
  • [20] T. Kaczorek: Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems, 58(6), (2011), 1203-1210.
  • [21] T. Kaczorek: Positivity and stability of discrete-time nonlinear systems. Proc. of 2nd IEEE Int. Conf. on Cybernetics CYBCONF, 24-26 June, (2015), Gdynia, Poland.
  • [22] T. Kaczorek: Positive singular discrete time linear systems. Bulletin of the Polish Academy of Sciences - Technical Sciences, 45(4), (1997), 619-631.
  • [23] T. Kaczorek: Vectors and Matrices in Automation and Electrotechnics. WNT, Warszawa, 1998, (in Polish).
  • [24] T. Kaczorek and J. Klamka: Minimum energy control of 2D linear systems with variable coefficients. Int. J. of Control, 44(3), (1986), 645-650.
  • [25] J. Klamka: Controllability of Dynamical Systems. Kluwer Academic Press, Dordrecht, 1991.
  • [26] J. Klamka: Minimum energy control of 2D systems in Hilbert spaces. System Sciences, 9(1-2), (1983), 33-42.
  • [27] J. Klamka: Relative controllability and minimum energy control of linear systems with distributed delays in control. IEEE Trans. Automatic Control, 21(4), (1976), 594-595.
  • [28] V. Kucera and P. Zagalak: Fundamental theorem of state feedback for singular systems. Automatica, 24(5), (1988), 653-658
  • [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] 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
Typ dokumentu
Bibliografia
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