Canonical forms of singular 1D and 2D linear systems

• Autorzy: Tadeusz Kaczorek
• 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.

Słowa kluczowe

EN

canonical form; transformation; singular; 2D Roesser model; 1D system

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: 13
• Numer: 1
• Strony: 61-72

Daty

wydano

2003

otrzymano

2002-09-01

poprawiono

2003-01-01

Twórcy

autor

Tadeusz Kaczorek

• Warsaw University of Technology, Faculty of Electrical Engineering, Institute of Control and Industrial Electronics, 00-662 Warszawa, Koszykowa 75, Poland

Bibliografia

• Aplevich J.D. (1985): Minimal representations of implicit linear systems. - Automatica, Vol. 21, No. 3, pp. 259-269.
• Brunovsky P.A. (1970): A classification of linear controllable systems. - Kybernetika, Vol. 6, No. 3, pp. 173-187.
• Cobb D. (1984): Controllability, observability and duality in singular systems. - IEEE Trans. Automat. Contr., Vol. A-26, No. 12, pp. 1076-1082.
• Dai L. (1989): Singular Control Systems. - New York: Springer.
• Eising R. (1978): Realization and stabilization of 2-D systems. - IEEE Trans. Automat. Contr., Vol. AC-23, No. 5, pp. 795-799.
• Fornasini E. and Marchesini G. (1976): State-space realization theory of two-dimensional filters. - IEEE Trans. Automat. Contr., Vol. AC-21, No. 4, pp. 484-491.
• Fornasini E. and Marchesini G. (1978): Doubly-indexed dynamical systems: State-space models and structural properties. - Math. Syst. Theory, Vol. 12, pp. 59-72.
• Gałkowski K. (1981): The state-space realization of an n-dimensional transfer function. - Int. J. Circ. Theory Appl., Vol. 9, pp. 189-197.
• 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.
• 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.
• 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.
• 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.
• Kaczorek T. (1985): Two-Dimensional Linear Systems. - Berlin: Springer.
• 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.
• 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.
• Kaczorek T. (1992): Linear Control Systems, Vols. 1 and 2. - New York: Wiley.
• 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.
• Kaczorek T. (1996): Reachability and controllability of non-negative 2-D Roesser type models. - Bull. Pol. Acad. Sci. Techn. Sci., Vol. 44, No. 4, pp. 405-410.
• 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.
• Kaczorek T. (1997b): Positive realization in canonical form of the 2D Roesser type model. - Proc. Control and Decision Conf., San Diego, pp. 335-336.
• Kaczorek T. (1997c): Realisation problem for positive 2D Roesser model. -Bull. Pol. Acad. Sci. Techn. Sci., Vol. 45, No. 4, pp. 607-619.
• Kaczorek T. (1998): Realisation problem for singular 2D linear systems.- Bull. Pol. Acad. Sci. Techn. Sci., Vol. 46, No. 3, pp. 317-330.
• Kaczorek T. (2000): Determination of realisations in canonical forms for singular linear. - Proc. Polish-Ukrainian School-Seminar, Solina, Poland, pp. 47-51.
• Klamka J. (1991): Controllability of Dynamical Systems. -Dordrecht: Kluwer.
• Kurek J. (1985): The general state-space model for a two-dimensional linear digital system. - IEEE Trans. Automat. Contr., Vol. AC-30, No. 6, pp. 600-602.
• Lewis F.L. (1984): Descriptor systems: Decomposition into forward and backward subsystems. - IEEE Trans. Automat. Contr., Vol. AC-29, No. 2, pp. 167-170.
• Lewis F.L. (1986): A survey of linear singular systems. - Circ. Syst. Signal Process., Vol. 5, No. 1, pp. 1-36.
• Lewis F.L. and Mertzios B.G. (1989): On the analysis of discrete linear time-invariant singular systems. - IEEE Trans. Automat. Contr., Vol. AC-34.
• Luenberger D.G. (1967): Canonical forms for linear multivariable systems. - IEEE Trans. Automat. Contr., Vol. AC-12, No. 63, pp. 290-293.
• Luenberger D.G. (1978): Time-invariant descriptor systems. - Automatica Vol. 14, pp. 473-480.
• Ozcaldiran K. and Lewis F.L. (1989): Generalized reachability subspaces for singular systems. - SIAM J. Contr. Optim., Vol. 26, No. 3, pp. 495-510.
• 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.
• Silverman L.M. (1966): Transformation of time- variable systems to canonical (phase-variable) form. - IEEE Trans. Automat. Contr., Vol. AC-11, No. 2, pp. 300-303.
• Valcher M.E. (1997): On the internal stability and asymptotic behavior of 2-D positive systems. - IEEE Trans. Circ. Syst. - I, Vol. 44, No. 7, pp. 602-613.
• Żak S.H., Lee E.B. and Lu W.-S. (1986): Realizations of 2-D filters and time delay systems. - IEEE Trans. Circ. Syst., Vol. CAS-33, No. 12, pp. 1241-1244.