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Computation of positive realizations of SISO singular hybrid linear systems

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EN
Abstrakty
EN
The realization problem for 2D positive singular linear hybrid systems is formulated, as well as a method based on the state variable diagram for finding a positive realization of a given improper transfer function is proposed. Sufficient conditions for the existence of a positive realization of a given improper transfer function are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.
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autor
  • Professor at Białystok Technical University, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland, kaczorek@isep.pw.edu.pl
Bibliografia
  • [1] Benvenuti L., Farina L., “A tutorial on the positive realization problem”,IEEE Trans. Autom. Control , vol. 49, no. 5, 2004, pp. 651-664.
  • [2] Farina L., Rinaldi S.,Positive Linear Systems; Theory and Applications, J. Wiley: New York, 2000.
  • [3] Kaczorek T., Busłowicz M., “Reachability and minimum energy control of positive linear discrete-time systems with one delay”. In:12 Mediterranean Conference on Control and Automation, 6 -9 June, 2004, Kusadasi,Izmir, Turkey.
  • [4] Kaczorek T., Busłowicz M., “Minimal realization problem for positive multivariable linear systems with delay”,Int. J. Appl. Math. Comput. Sci., vol. 14, no. 2, 2004, pp.181-187.
  • [5] Kaczorek T., Sajewski Ł., “Computation of positive realization of MIMO hybrid linear systems with delays using the state variable diagram method”. In:16 International Conference on Systems Science, 4 6 September,2007, Wrocław, vol. 1, 2007, pp. 150-160.
  • [6] Kaczorek T., Sajewski Ł., “Computation of positive realization of MIMO hybrid linear systems using the state variable diagram method”, , vol. 17, no. 1, 2007, pp. 5-21.
  • [7] Kaczorek T., Sajewski Ł., “Realization problem for positive 2D hybrid systems with one delay in state and input vectors”. In:8 International Workshop „Computational Problems of Electrical Engineering, 14 -16 September 2007, Wilkasy, Poland, , no.2, 2007, pp. 242-246.
  • [8] Kaczorek T., “Some recent developments in positive systems”. In:Proc. of 7 Conference of Dynamical Systems Theory and Applications, Łódź 2003 pp. 25-35.
  • [9] Kaczorek T., Positive 1D and 2D systems, Springer Verlag: London 2002.
  • [10] Kaczorek T., “A realization problem for positive continues-time linear systems with reduced numbers of delay”,Int. J. Appl. Math. Comp. Sci., vol. 16, no. 3, 2006, pp. 325-331.
  • [11] Kaczorek T., “Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs” ,Int. J. Appl. Math. Comp. Sci., vol. 16, no. 2, 2006, pp. 101-106.
  • [12] Kaczorek T., “Realization problem for positive discretetime systems with delay” , System Science, vol. 30, no. 4, 2004, pp. 117-130.
  • [13] Kaczorek T., “Positive minimal realizations for singular discrete-time systems with delays in state and delays in control” ,Bull. Pol. Acad. Sci. Techn, vol 53, no 3, 2005, pp. 293-298.
  • [14] Kaczorek T., “Positive 2D hybrid linear systems”. In:Proc. Inter. Conf. Numerical Linear Algebra in Signals Systems and Control 2007.
  • [15] Kaczorek T., “Realization problem for positive 2D hybrid systems”, Submitted to COMPEL.
  • [16] Kaczorek T., Two-Dimensional Linear Systems, Springer Verlag: Berlin 1985.
  • [17] Kaczorek T.,Determination of singular positive realization of improper transfer function of 2D linear systems ,SMC Zakopane 2007.
  • [18] Klamka J., Controllability of Dynamical Systems, Kluwer Academic Publ.: Dordrecht, 1991.
  • [19] Kurek J., “The general state-space model for a two-dimensional linear digital system”,IEEE Trans. Austom. Contr. AC-30, June 1985, pp. 600-602.
  • [20] Marchenko V. M., Poddubnaya O. N., “Relative controllability of stationary hybrid systems”. In:10 IEEE Int.Conf. on Methods and Models in Automation and Robotics, 30th August - 2nd Sept. 2004, Międzyzdroje, Poland,pp. 267-272.
  • [21] Marchenko V. M., Poddubnaya O. N., Zaczkiewicz Z., “On the observability of linear differential-algebraic systems with delays”, IEEE Trans. Autom. Contr., vol. 51, no. 8, 2006, pp. 1387-1392.
  • [22] Roesser R. B., “A discrete state-space model for linear image processing”,IEEE Trans. on Automatic Control AC-20, no. 1, 1975, pp. 1-10.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ6-0028-0002
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