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Computation of positive realizations of singular hybrid linear systems - two cases

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EN
Abstrakty
EN
The realization problem for 2D positive linear hybrid systems is addressed. Two methods based on the state variable diagram for finding positive realizations of a given improper transfer function are proposed. Sufficient conditions for the existence of a positive realization of a given improper transfer function are established. Procedures for computation of a positive realization are proposed and illustrated by numerical examples.
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27--39
Opis fizyczny
Bibliogr. 22 poz.
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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., Minimal realization problem for positive multivariable linear systems with delay, Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 2, 2004, pp. 181-187.
  • [4] Kaczorek T., Busłowicz M., Reachability and minimum energy control of positive linear discrete-time systems with one delay, 12th Mediterranean Conference on Control and Automation, June 6-9, 2004, Kusadasi, Izmir, Turkey.
  • [5] Kaczorek T., Sajewski L., Computation of positive realization of MIMO hybrid linear systems using the state variable diagram method, Archives of Control Sciences, Vol. 17, No. 1, 2007, pp. 5-21,
  • [6] Kaczorek T., A realization problem for positive continuous-time linear systems with reduced numbers of delay, Int. J. Appl. Math. Comp. Sci., Vol. 16, No. 3, 2006, pp. 325-331.
  • [7] Kaczorek T., Canonical forms of singular ID and 2D linear systems, Int. J. Appl. Math. Comput. Sci., Vol. 13, No. 1, 2003, pp. 61-72.
  • [8] Kaczorek T., Determination of singular positive realization of improper transfer function of 2D linear systems, SMC Zakopane, 2007.
  • [9] Kaczorek T., Positive ID and 2D systems, Springer Verlag, London, 2002.
  • [10] Kaczorek T., Positive 2D hybrid linear systems, Bull. Pol. Acad. of Sci., Techn. Sci., Vol. 55, No. 5, 2007, pp. 351-358.
  • [11] 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.
  • [12] Kaczorek T., Realization problem for positive 2D hybrid systems, International Journal for Computation and Mathematics in Electrical and Electronic Engineering, COMPEL, Vol. 27, No. 3, 2008, pp. 613-623.
  • [13] Kaczorek T., Realization problem for positive discrete-time systems with delay, System Science, Vol. 30, No. 4, 2004, pp. 117-130.
  • [14] 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.
  • [15] Kaczorek T., Some recent developments in positive systems, Proc. 7th Conference of Dynamical Systems Theory and Applications, Łódź 2003. pp. 25-35.
  • [16] Kaczorek T., Two-Dimensional Linear Systems, Springer Verlag, Berlin, 1985.
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  • [18] 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.
  • [19] 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.
  • [20] Marchenko V.M., Poddubnaya O.N., Relative controllability of stationary hybrid systems, 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics, 30 Aug.-2 Sept. 2004, Międzyzdroje, Poland, pp. 267-272.
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  • [22] Valcher M.E., On the initial stability and asymptotic behaviour of 2D positive systems, IEEE Trans, on Circuits and Systems, I, Vol. 44, No. 7, 1997, pp. 602-613.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0062-0004
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