Inverse systems of linear systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

The concept of inverse systems for standard and positive linear systems is introduced. Necessary and sufficient conditions for the existence of the positive inverse system for continuous-time and discrete-time linear systems are established. It is shown that: 1) The inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable. 2) The inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. 3) The inverse system of continuous-time and discrete-time linear systems are reachable if and only if the standard systems are reachable. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

inverse system; linear system; positive system; reachability; stability

PL

system odwrotny; system liniowy; system dodatni; osiągalność; stabilność

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2010
• Tom: Vol. 59, nr 3-4
• Strony: 203--216
• Opis fizyczny: Bibliogr. 9 poz.,

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351 Białystok,

Bibliografia

• [1] P.J. Antsaklis, A.N. Michel, Linear Systems. Birkhauser, Boston 2006.
• [2] L. Farina, S. Rinaldi, Positive Linear Systems. Theory and Applications. J. Wiley, New York 2000.
• [3] F.R. Gantmacher, The Theory of matrices. Chelsea 1960.
• [4] T. Kaczorek, Positive 1D and 2D Systems. Springer Verlag, London 2001.
• [5] T. Kaczorek, Linear Control Systems. Vol. 1, J. Wiley, New York 1999.
• [6] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics. WNT, Warszawa 1998 (in Polish).
• [7] T. Kailath, Linear Systems. Prentice-Hall, Englewood Cliffs, New York 1980.
• [8] H. Rosenbrock, State-Space and Multivariable Theory. J. Wiley, New York 1970.
• [9] S.H. Zak, Systems and Control. Oxford University Press, New York 2003.