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Computation of positive realizations of MIMO hybrid linear systems with delays using the state variable diagram method

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The realization problem for 2D positive multi-input and multi-output (MIMO) linear hybrid systems with delays in state vector and input is addressed. A method based on the state variable diagram for finding positive realizations of a given proper transfer matrix is proposed. Sufficient conditions for the existence of a positive realization of a given proper transfer matrix are established. A procedure for computation of a positive realization is proposed and illustrated by a numerical example.
Czasopismo
Rocznik
Strony
5--13
Opis fizyczny
Bibliogr. 18 poz., rys.
Twórcy
autor
autor
  • Institute of Control and Industrial Electronics, Warsaw Technical University, Koszykowa 75, 00-662 Warsaw, 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., Bustowicz M., Reachability and minimum energy control of positive linear discrete-time systems with one delay, 12th Mediterranean Conf. Control and Automation, June 6-9,2004, Kusadasi, Izmir, Turkey.
  • [4] Kaczorek T., Some recent developments in positive systems, Proc. 7th Conf. Dynamical Systems Theory and Applications, Łódź 2003, pp. 25-35.
  • [5] Kaczorek T., Positive ID and 2D systems, Springer Verlag, London 2002.
  • [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., 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.
  • [8] Kaczorek T., Realization problem for positive discrete-time systems with delay. System Science, Vol. 30, No. 4, 2004, pp. 117-130.
  • [9] 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.
  • [10] 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.
  • [11] Kaczorek T., Positive 2D hybrid linear systems, Proc. Inter. Conf. Numerical Linear Algebra in Signals Systems and Control, 2007.
  • [12] Kaczorek T., Realization problem for positive 2D hybrid systems. Submitted to COMPEL.
  • [13] Klamka J., Controllability of Dynamical Systems, Kluwer Academic Publ., Dordrecht 1991.
  • [14] Kurek J., The general state-space model for a two-dimensional linear digital system, IEEE Trans. Autom. Contr, AC-30, June 1985, pp. 600-602.
  • [15] Marchenko V.M., Poddubnaya O.N., Relative controllability of stationary hybrid systems, 10th IEEE Int. Conf. Methods and Models in Automation and Robotics, 30 August-2 September 2004, Międzyzdroje, Poland, pp. 267-272.
  • [16] 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.
  • [17] Roesser R.B., A discrete state-space model for linear image processing, IEEE Trans, on Automatic Control, AC-20, 1, 1975, pp. 1-10.
  • [18] Valcher M.E., On the initial stability and asymptotic behavior 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-BAT5-0033-0045
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