Computation of positive realization of MIMO hybrid linear systems in the form of second Fornasini-Marchesini model

• Autorzy: Kaczorek T. , Sajewski Ł.
• Języki publikacji: EN

Abstrakty

EN

The realization problem for positive multi-input and multi-output (MIMO) linear hybrid systems with the form of second Fornasini-Marchesini model is formulated and a method based on the state variable diagram for finding a positive realization of a given proper transfer matrix is proposed. Sufficient conditions for the existence of the 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.

Słowa kluczowe

EN

hybrid; 2D system; positive; realization; existence; computation

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2010
• Tom: Vol. 20, no. 3
• Strony: 267--285
• Opis fizyczny: Bibliogr. 18 poz., rys., wzory

Twórcy

autor

Kaczorek T.

autor

Sajewski Ł.

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

Bibliografia

• [1] L. BENVENUTI and L. FARINA: A tutorial on the positive realization problem. IEEE Trans. Autom. Control, 49(5), (2004), 651-664.
• [2] L. FARINA and S. RINALDI: Positive linear systems. Theory and applications. J. Wiley, New York, 2000.
• [3] T. KACZOREK and M. BUSŁOWICZ: Reachability and minimum energy control of positive linear discrete-time systems with one delay. 12th Mediterranean Conf. On Control and Automation, Kusadasi, Izmir, Turkey, (2004).
• [4] T. KACZOREK: Some recent developments in positive systems. Proc. 7th Conf. Of Dynamical Systems Theory and Applications, , Łódz, Poland, (2003), 25-35.
• [5] T. KACZOREK: Positive 1D and 2D systems. Springer Verlag, London, 2002.
• [6] T. KACZOREK: A realization problem for positive continuous-time linear systems with reduced numbers of delay. Int. J. Appl. Math. Comp. Sci.,1-6(3), (2006), 325-331.
• [7] T. KACZOREK: Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. Int. J. Appl. Math. Comp. Sci., 16(2), (2006), 101-106.
• [8] T. KACZOREK: Realization problem for positive discrete-time systems with delay. System Science, 30(4), (2004), 117-130.
• [9] T. KACZOREK: Positive minimal realizations for singular discrete-time systems with delays in state and delays in control. Bull. Pol. Acad. Sci. Techn., 53(3), (2005), 293-298.
• [10] T. KACZOREK and M. BUSŁOWICZ: Minimal realization problem for positive multivariable linear systems with delay. Int. J. Appl. Math. Comput. Sci., 14(2), (2004), 181-187.
• [11] T. KACZOREK: Positive 2D hybrid linear systems. Bull. Pol. Acad. Sci. Techn., 55(4), (2007), 351-358.
• [12] T. KACZOREK: Realization problem for positive 2D hybrid systems. COMPEL: The Int. J. for Computation and Mathematics in Electrical and Electronic Engineering, 27(3), (2008), 613-623.
• [13] J. KLAMKA: Controllability of dynamical systems. Kluwer Academic Publ., Dordrecht, 1991.
• [14] J. KUREK: The general state-space model for a two-dimensional linear digital system. IEEE Trans. Austom. Contr., AC-30 (1985), 600-602.
• [15] V. M. MARCHENKO and O. N. PODDUBNAYA: Relative controllability of stationary hybrid systems. 10th IEEE Int. Conf. on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, (2004), 267-272.
• [16] V. M. MARCHENKO, O. N. PODDUBNAYA and Z. ZACZKIEWICZ: On the observability of linear differential-algebraic systems with delays. IEEE Trans. Autom. Contr., 51(8), (2006), 1387-1392.
• [17] R. B. ROESSER: A discrete state-space model for linear image processing. IDEE Trans. on Autom. Contr., AC-20(1), (1975), 1-10.
• [18] M. E. VALCHER: On the initial stability and asymptotic behavior of 2D positive systems. IEEE Trans. on Circuits and Systems, I, 44(7), (1997), 602-613.