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Tytuł artykułu

Canonical Forms of Singular 1 D and 2 D Linear Systems

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical forms for a given 2D transfer function is presented. Necessary and sufficient conditions for the existence of a pair of nonsingular block diagonal matrices transforming the matrices of the singular 2D Roesser model to their canonical forms are established. A procedure for computing the pair of nonsingular matrices is presented.
Rocznik
Strony
61--72
Opis fizyczny
Bibliogr. 35 poz., rys.
Twórcy
autor
  • Warsaw University of Technology Faculty of Electrical Engineering Institute of Control and Industrial Electronics 00-662 Warszawa, Koszykowa 75, Poland, kaczorek@isep.pw.edu.pl
Bibliografia
  • [1] Aplevich J.D. (1985): Minimal representations of implicit linear systems. — Automatica, Vol. 21, No. 3, pp. 259–269.
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  • [8] Gałkowski K. (1981): The state-space realization of an ndimensional transfer function. — Int. J. Circ. Theory Appl., Vol. 9, pp. 189–197.
  • [9] Gałkowski K. (1992): Transformation of the transfer function variables of the singular n-dimensional Roesser model.—Int. J. Circ. Theory Appl., Vol. 20, pp. 63–74.
  • [10] Gałkowski K. (1997): Elementary operation approach to state-space realizations of 2-D systems. — IEEE Trans. Circ. Syst. Fund. Theory Appl., Vol. 44, No. 2, pp. 120–129.
  • [11] Hayton G.E., Walker A.B. and Pugh A.C. (1988): Matrix pencil equivalents of a general polynomial matrix. — Int. J. Contr., Vol. 49, No. 6, pp. 1979–1987.
  • [12] Hinamoto T. and Fairman F.W. (1984): Realisation of the Attasi state space model for 2-D filters. — Int. J. Syst. Sci., Vol. 15, No. 2, pp. 215–228.
  • [13] Kaczorek T. (1985): Two-Dimensional Linear Systems. — Berlin: Springer.
  • [14] Kaczorek T. (1987): Realization problem for general model of two-dimensional linear systems. — Bull. Pol. Acad. Sci. Techn. Sci., Vol. 35, No. 11–12, pp. 633–637.
  • [15] Kaczorek T. (1988): Singular general model of 2-D systems and its solution. — IEEE Trans. Automat. Contr., Vol. AC–33, No. 11, pp. 1060–1061.
  • [16] Kaczorek T. (1992): Linear Control Systems, Vols. 1 and 2. — New York: Wiley.
  • [17] Kaczorek T. (1995): Singular 2-D continuous-discrete linear systems. Dynamics of continuous, discrete and impulse systems.— Adv. Syst. Sci. Appl., Vol. 1, No. 1, pp. 103–108.
  • [18] Kaczorek T. (1996): Reachability and controllability of nonnegative 2-D Roesser type models.—Bull. Pol. Acad. Sci. Techn. Sci., Vol. 44, No. 4, pp. 405–410.
  • [19] Kaczorek T. (1997a): Positive realisations of improper transfer matrices of discrete-time linear systems. — Bull. Pol. Acad. Techn. Sci., Vol. 45, No. 2, pp. 277–286.
  • [20] Kaczorek T. (1997b): Positive realization in canonical form of the 2D Roesser type model. — Proc. Control and Decision Conf., San Diego, pp. 335–336.
  • [21] Kaczorek T. (1997c): Realisation problem for positive 2D Roesser model. — Bull. Pol. Acad. Sci. Techn. Sci., Vol. 45, No. 4, pp. 607–619.
  • [22] Kaczorek T. (1998): Realisation problem for singular 2D linear systems. — Bull. Pol. Acad. Sci. Techn. Sci., Vol. 46, No. 3, pp. 317–330.
  • [23] Kaczorek T. (2000): Determination of realisations in canonical forms for singular linear. — Proc. Polish-Ukrainian School–Seminar, Solina, Poland, pp. 47–51.
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  • [25] Kurek J. (1985): The general state-space model for a twodimensional linear digital system. — IEEE Trans. Automat. Contr., Vol. AC–30, No. 6, pp. 600–602.
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  • [27] Lewis F.L. (1986): A survey of linear singular systems. — Circ. Syst. Signal Process., Vol. 5, No. 1, pp. 1–36.
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  • [29] Luenberger D.G. (1967): Canonical forms for linear multivariable systems. — IEEE Trans. Automat. Contr., Vol. AC–12, No. 63, pp. 290–293.
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  • [32] Roesser R.B. (1975): A discrete state space model for linear image processing.—IEEE Trans. Automat. Contr., Vol. AC–20, No. 1, pp. 1-10.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0002-0006
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