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Minimum energy control of positive 2D continuous-discrete linear systems with bounded inputs

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Treść / Zawartość
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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new formulation of the minimum energy control problem for the positive 2D continuousdiscrete linear systems with bounded inputs is proposed. Necessary and sufficient conditions for the reachability of the systems are established. Conditions for the existence of the solution to the minimum energy control problem and a procedure for computation of an input minimizing the given performance index are given. Effectiveness of the procedure is demonstrated on numerical example.
Rocznik
Strony
319--331
Opis fizyczny
Bibliogr. 34 poz., wykr., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok
Bibliografia
  • [1] Y. Bistritz: A stability test for continuous-discrete bivariate polynomials. Proc. Int. Symp. on Circuits and Systems, 3 (2003), 682-685.
  • [2] M. Busłowicz: Stability and robust stability conditions for a general model of scalar continuous-discrete linear systems. Measurement Automation and Monitoring, 56(2), (2010), 133-135.
  • [3] Busłowicz: Robust stability of the new general 2D model of a class of continuous-discrete linear systems. Bulletin of the Polish Academy of Sciences Technical Sciences, 58(4), (2010), 561-565.
  • [4] M. Dymkov, I. Gaishun, E. Rogers, K. Gałkowski and D. H. Owens: Control theory for a class of 2D continuous-discrete linear systems. Int. J. Control, 77(9), (2004), 847-860.
  • [5] L. Farina and S. Rinaldi: Positive Linear Systems; Theory and Applications. J. Wiley, New York, 2000.
  • [6] K. GAałkowski, E. Rogers, W. Paszke and D. H. Owens: Linear repetitive process control theory applied to a physical example. Int. J. of Applied Mathematics and Computer Science, 13(1), (2003), 87-99.
  • [7] T. Kaczorek: Minimum energy control of fractional positive continuous-time linear systems. Proc. of Int. Conf. on Methods and Models in Automation and Robotics, Mi˛edzyzdroje, Poland, (2013).
  • [8] T. Kaczorek: Minimum energy control of descriptor positive discrete-time linear systems. COMPEL – The Int. J. for Computation and Mathematics in Electrical and Electronic Engineering, 33(3), (2014), 976-988.
  • [9] T. Kaczorek: Minimum energy control of positive continuous-time linear systems. Int. J. of Applied Mathematics and Computer Science, (in Press).
  • [10] T. KACZOREK: Minimum energy control of positive continuous-time linear systems with bounded inputs. Int. J. of Applied Mathematics and Computer Science, (in Press).
  • [11] T. Kaczorek: Minimum energy control of positive discrete-time linear systems with bounded inputs. Proc. Int. Conf. on Mathematical Methods in Engineering, Porto, Portugal, (2013).
  • [12] T. Kaczorek: Minimum energy control of positive fractional continuous-time linear systems. Bulletin of the Polish Academy of Sciences Technical Sciences, (in Press).
  • [13] T. Kaczorek: Minimum energy control of positive fractional descriptor continuous-time linear systems. IET Control Theory & Applications, 8(4), (2014), 219-225.
  • [14] T. Kaczorek: New stability tests of positive standard and fractional linear systems. Circuit and Systems, 2(4), (2011), 261-268.
  • [15] T. Kaczorek: Positive 1D and 2D systems. Springer Verlag, London, 2001.
  • [16] T. Kaczorek: Positive 2D hybrid linear systems. Bulletin of the Polish Academy of Sciences Technical Sciences, 55(4), (2007), 351-358.
  • [17] T. Kaczorek: Positive fractional 2D continuous-discrete linear systems. Bulletin of the Polish Academy of Sciences Technical Sciences, 59(4), (2011), 575- 579.
  • [18] T. Kaczorek: Positive fractional 2D hybrid linear systems. Bulletin of the Polish Academy of Sciences Technical Sciences, 56(3), (2008), 273-277.
  • [19] T. Kaczorek: Reachability and minimum energy control of positive 2D continuous-discrete systems. Bulletin of the Polish Academy of Sciences Technical ciences, 46(1), (1998), 85-93.
  • [20] T. Kaczorek: Realization problem for positive 2D hybrid systems. COMPEL – The Int. J. for Computation and Mathematics in Electrical and Electronic Engineering, 27(3), (2008), 613-623.
  • [21] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer- Verlag, Berlin, 2012.
  • [22] T. Kaczorek: Stability of continuous-discrete linear systems described by general model. Bulletin of the Polish Academy of Sciences Technical Sciences, 59(2), (2011), 189-193.
  • [23] T. Kaczorek and J. Klamka: Minimum energy control of 2D linear systems with variable coefficients. Int. J. of Control, 44(3), (1986), 645-650.
  • [24] J. Klamka: Controllability and minimum energy control problem of fractional discrete-time systems. Chapter in "New Trends in Nanotechology and Fractional Calculus", Eds. Baleanu D., Guvenc Z. B., Tenreiro Machado J. A., Springer-Verlag, New York, 2010, 503-509.
  • Calculus", Eds. Baleanu D., Guvenc Z.B., Tenreiro Machado J.A., Springer-Verlag, New York, 2010, 503-509.
  • [25] J. Klamka: Controllability of Dynamical Systems. Kluwer Academic Press, Dordrecht, 1991.
  • [26] J. Klamka: Controllability of dynamical systems-a survey. Archives of Control Sciences, 2(3-4), (1993), 281-307.
  • [27] J. Klamka: Minimum energy control of 2D systems in Hilbert spaces. Systems Science, 9(1-2), (1983), 33-42.
  • [28] J. Klamka: Minimum energy control of discrete systems with delays in control. Int. J. of Control, 26(5), (1977), 737-744.
  • [29] J. Klamka: Relative controllability and minimum energy control of linear systems with distributed delays in control. IEEE Trans. on Automatic Control, 21(4), (1976), 594-595.
  • [30] T. Kaczorek, V. Macharenko and L. Sajewski: Solvability of 2D hybrid linear systems - comparison of three different methods. Acta Mechanica et Automatica, 2(2), (2008), 59-66.
  • [31] K. S. Narendra and R. Shorten: Hurwitz stability of Metzler matrices. IEEE Trans. on Automatic Control, 55(6), (2010), 1484-1487.
  • [32] L. Sajewski: Solution of 2D singular hybrid linear systems. Kybernetes, 38(7-8), (2009), 1079-1092.
  • [33] Y. Xiao: Stability test for 2-D continuous-discrete systems. Proc. 40th IEEE Conf. on Decision and Control, 4 (2001), 3649-3654.
  • [34] Y. Xiao: Stability, controllability and observability of 2-D continuous-discrete systems. Proc. Int. Symp. on Circuits and Systems, 4 (2003), 468-471.
Uwagi
EN
This work has been supported with a grant from the Polish Ministry of Science and High Education under work S/WE/1/11
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2d7c7132-ce2c-456e-ae1a-567217e0ff57
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