Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models with state-feedbacks

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Necessary and sufficient conditions are established for the pointwise completeness of 2D standard and positive Fornasini-Marchesini models with state-feedbacks. Similar relations are obtained for the pointwise degeneracy of the 2D models with state-feedbacks. It is shown that if the positive 2D model is pointwise complete then there exists a gain matrix of the state-feedback such that the closed-loop system is pointwise degenerated if both matrices B1 and B2 of the 2D Fornasini-Marchesini model are nonzero. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

pointwise completeness; standard; state-feedbacks

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2011
• Tom: Vol. 40, no 1
• Strony: 39--58
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok University of Technology, Białystok, Poland

Bibliografia

• BUSŁOWICZ, M. (2008) Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order. Zesz. Nauk. Pol Śląskiej, Automatyka, 151, 19-24 (in Polish).
• BUSŁOWICZ, M., KOCISZEWSKI, R. and TRZASKO, W. (2006) Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays. Zesz. Nauk. Pol. Śląskiej, Automatyka, 145, 55-56 (in Polish).
• CHOUNDHURY, A.K. (1972) Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems. Int. J. Control, 16 (6), 1083-1100.
• FARINA, L. and RINALDI, S. (2000) Positwe Linear Systems; Theory and Applications. J. Wiley, New York.
• FORNASINI, E. and MARCHESINI, G. (1976) State-space realization theory of two-dimensional filters. IEEE Trans. Autom. Contr., AC-21, 484-491.
• FORNASINI, E. and MARCHESINI, G. (1978) Double indexed dynamical systems. Math. Sys. Theory, 12, 59-72.
• KACZOREK, T. (1985) Two-Dimensional Linear Systems. Springer Verlag, Berlin.
• KACZOREK, T. (2002) Positve ID and 2D Systems. Springer-Verłag, London.
• KACZOREK, T. (2007) Polynomial and Rational Matrices. Applications in Dynamical Systems Theory. Springer-Yerlag, London.
• KACZOREK, T. (2009) Pointwise completeness and pointwise degeneracy of standard and positive fractional linear systems with state-feedbacks. Archives of Control Sciences, 19, 295-306.
• KACZOREK, T. (2010a) Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state-feedbacks. Journal of Automation, Mobile Robotics & Intelligent Systems, 4 (1), 3-7.
• KACZOREK, T. (2010b) Pointwise completeness and pointwise degeneracy of 2D standard and positive Fornasini-Marchesini models. COMPEL (submitted).
• KACZOREK T. and BUSŁOWICZ M. (2009) Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems. Journal of Automation, Mobile Robotics & Intelligent Systems, 3 (1), 8-11.
• KUREK, J. (1985) The general state-space model for a two-dimensional linear digital systems. IEEE Trans. Autom. Contr., AC-30, 600-602.
• OLBROT, A. (1972) On degeneracy and related problems for linear constant time-lag systems. Ricerche di Automatica, 3 (3), 203-220.
• POPOV, V.M. (1972) Pointwise degeneracy of linear time-invariant delay-differential equations. Journal of Diff. Equations, 11, 541-561.
• ROESSER, R.P. (1975) A discrete state-space model for linear image processing. IEEE Trans, on Automatic Control, AC-20 (1), 1-10.
• TRZASKO, W., BUSŁOWICZ, M. and KACZOREK, T. (2007) Pointwise completeness of discrete-time cone-systems with delays. Proc. EUROCON 2007, Warsaw, 606-611.
• WEISS, L. (1970) Controllability for various linear and nonlinear systems models. Lecture Notes in Mathematics, 144, Seminar on Differential Equations and Dynamie System II. Springer, Berlin, 250-262.