Stability of continuous-time and discrete-time linear systems

• Autorzy: Kaczorek T. , Borawski K.
• Języki publikacji: EN

Abstrakty

EN

The inverse Frobenius matrices and the characteristic equations of the inverse systems are investigated. It is shown that the inverse system of continuous-time linear system is asymptotically stable if and only if the standard system is asymptotically stable and the inverse system of discrete-time linear system is asymptotically stable if and only if the standard system is unstable. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

Frobenius matrix; continuous-time system; discrete-time system; linear; stability; state matrix

• Wydawca: Wydawnictwo PAK
• Czasopismo: Measurement Automation Monitoring
• Rocznik: 2016
• Tom: Vol. 62, No. 4
• Strony: 132--135
• Opis fizyczny: Bibliogr. 14 poz., wzory

Twórcy

autor

Kaczorek T.

• Bialystok University of Technology, Faculty of Electrical Engineering, 45d Wiejska Str., 15-351 Białystok

autor

Borawski K.

• Bialystok University of Technology, Faculty of Electrical Engineering, 45d Wiejska Str., 15-351 Białystok

Bibliografia

• [1] Antsaklis P. J., Michel A. N.: Linear Systems, Birkhauser, Boston 2006.
• [2] Busłowicz M.: Simple stability conditions for linear positive discrete-time systems with delays, Bulletin of the Polish Academy of Sciences. Technical Sciences, vol. 56, no. 4, 2008, 325-328.
• [3] Busłowicz M.: Stability of state-space models of linear continuous-time fractional order systems, Acta Mechanica et Automatica, vol. 5, no. 2, 2011, 12-15.
• [4] Busłowicz M., Kaczorek T.: Simple conditions for practical stability of positive fractional discrete-time linear systems, Int. J. of Applied Mathematics and Computers Science, vol. 19, no. 2, 2009, 263-269.
• [5] Gantmacher F. R.: The Theory of Matrices. Chelsea Pub. Comp., London, 1959.
• [6] Kaczorek T.: Inverse systems of linear systems, Archives of Electrical Engineering, vol. 59, no. 3-4, 2010, 203-216.
• [7] Kaczorek T.: Linear Control Systems, Vol. 1, J. Wiley, New York, 1999.
• [8] Kaczorek T.: Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
• [9] Kaczorek T.: Selected Problems of Fractional Systems Theory, Springer-Verlag, Berlin 2012.
• [10] Kaczorek T.: Stability of positive continuous-time linear systems with delays, Bulletin of the Polish Academy of Sciences. Technical Sciences, vol. 57, no. 4, 2009, 395-398.
• [11] Kaczorek T.: Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa 1998 (in Polish).
• [12] Kailath T.: Linear Systems, Prentice-Hall, Englewood Cliffs, New York, 1980.
• [13] Rosenbrock H.: State-Space and Multivariable Theory, J. Wiley, New York, 1970.
• [14] Żak S.H., Systems and Control, Oxford University Press, New York, 2003.

Uwagi

EN

This work was supported by National Science Centre in Poland under work No. 2014/13/B/ST7/03467.

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę