Dynamical properties of Metzler systems

• Autorzy: Mitkowski W.
• Języki publikacji: EN

Abstrakty

EN

Spectral properties of nonnegative and Metzler matrices are considered. The conditions for existence of Metzler spectrum in dynamical systems have been established. An electric RL and GC ladder-network is presented as an example of dynamical Metzler system. The suitable conditions for parameters of these electrical networks are formulated. Numerical calculations were done in MATLAB.

Słowa kluczowe

EN

Metzler matrices; ladder and ring electrical networks; nonnegative matrices; positive linear systems

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2008
• Tom: Vol. 56, nr 4
• Strony: 309--312
• Opis fizyczny: Bibliogr. 13 poz., rys.

Twórcy

autor

Mitkowski W.

• Department of Automatics, AGH University of Science and Technology, 30 Mickiewicza Ave, 30-059 Kraków, Poland

Bibliografia

• [1] F.R. Gantmaher, Theory of Matrix, 4 ed., Nauka, Moskwa, 1988, (in Russian).
• [2] H. Minc, Nonnegative Matrices, J. Wiley, New York, 1988.
• [3] T. Kaczorek, Positive 1D and 2D Systems, Springer, London, 2002.
• [4] T. Kaczorek, “Computation of realizations of discrete-time cone systems”, Bull. Pol. Ac.: Tech. 54 (3), 347–350 (2006).
• [5] W. Mitkowski, “Remarks on stability of positive linear systems”, Control and Cybernetics 29 (1), 295–304 (2000).
• [6] T. Kaczorek, “Positive linear systems and their relationship with electrical circuits”, Proc. XX SPETO 2, 33–41 (1997).
• [7] T. Kaczorek, “Selected current research problems of positive 1D and 2D linear systems”, Proc. XIII KKA 1, 13–22 (1999), (in Polish).
• [8] A. Turowicz, Theory of Matrix. 6 ed., AGH, Kraków, 2005, (in Polish).
• [9] W. Mitkowski, “Similar systems to the positive systems”, Proc. XXIII IC-SPETO, 214–218 (2000), (in Polish).
• [10] W. Mitkowski, “Analysis of ladder network with boundary feedback”, Bull. Pol. Ac.: Tech. 35 (11–12), 695–699 (1987).
• [11] W. Mitkowski, “Analysis of ring network of RL and GC type”, Bull. Pol. Ac.: Tech. 40 (2), 135–138 (1992).
• [12] H. Górecki and A. Turowicz, “Analysis of an electric network chain with feedback”, Bull. Pol. Ac.: Tech. 21, 53–61 (1973).
• [13] T. Schanbacher, “Aspects of positivity in control theory”, SIAM J. Control and Optimization 27 (3), 457–475 (1989).