Singular Compartmental Linear Systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

Models of singular compartmental linear continuous-time and discrete-time systems are introduced. Solutions of the singular models in terms of the Drazin inverse of the models matrices are given. Necessary and sufficient conditions for the singular systems to be compartmental are established. A notion of P-equivalence is introduced and conditions for the P-equivalence of the compartmental and asymptotically stable positive system are derived.

Słowa kluczowe

EN

compartmental; singular; continous-time; discrete-time

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2003
• Tom: Vol. 51, nr 4
• Strony: 409--419
• Opis fizyczny: bibliogr. 15 poz.

Twórcy

autor

Kaczorek T.

• Institute of Control and Industrial Electronics Warsaw University of Technology, Faculty of Electrical Engineering, 00-662 Warszawa, Koszykowa 75, Poland (Instytut Sterowania i Elektroniki Przemysłowej, Politechnika Warszawska)

Bibliografia

• [1] L. Benvenuti, L. Farina, Positive and compartmental systems, IEEE Trans. on Autom. Control, 47, 2, (2002) 370-373.
• [2] R. Bru, C. Coll, E. Sanchez, Structural properties of positive linear time-invariant difference-algebraic equations, Linear Algebra and its Applications, 349 (2002) 1-10.
• [3] A. Berman, R. J. Plemmons, Nonnegative matrices in the mathematical science, Acadamic Press, New York 1979.
• [4] S. L. Campbell, C. D. Meyer, N. J. Rose, Applications of Drazin inverse to linear systems of differential equations with singular constant coefficients, SIAM J. Math., 31, 3, (1976) 411-425.
• [5] L, Farina, S. Rinaldi, Positive linear systems, John Wiley, New York 2000.
• [6] T. Kaczorek, Externally positive 2D linear systems, Bull. Pol. Ac. Tech., 47, 3,(1999) 227-234.
• [7] T. Kaczorek, Externally and internally positive time-varying linear systems, Intern. Journal of Applied Math. And Comp. Sci., 11, 4, (2001) 957-964.
• [8] T. Kaczorek, Positive 1D and 2D systems, Springer-Verlag London 2000.
• [9] T. Kaczorek, Externally and internally positive singular continuous-time linear systems, Machine Intelligence & Robotic Control, 3, 1, (2001) 1-6.
• [10] T. Kaczorek, Linear control systems, vol. I, Research Studies Press, J. Wiley, NY 1993.
• [11] D. G. Luengerger, Positive linear systems in introduction to dynamic systems, New York, J. Wiley, 1976.
• [12] Y. Ohta, H. Madea, S. Kodama, Reachability, observability and realizability of continuous-time positive systems, SIAM J, cotr, Optim., 22, 2, (...) 171-180.
• [13] V. G. Rumchev, D. J. G. James, Controllability of positive linear discrete-time systems, Intern. J. Control, 50, 2, (1989) 845-857.
• [14] E. Valcher, Controllability and reachability criteria for discrete-time positive system, Intern. J. Control, 65, 3, (1996) 511-536.
• [15] E. Valcher, On the internal stability and asymptotic behavior of 2-D positive systems, IEEE Trans. on Circuits and Systems, 44, 7, (1997) 602-613.