Analysis and comparison of the stability of discrete-time and continuous-time linear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/acsc-2016-0030

• Języki publikacji: EN

Abstrakty

EN

The asymptotic stability of discrete-time and continuous-time linear systems described by the equations x_i+1 = Ā^kx_i and x(t) = A^kx(t) for k being integers and rational numbers is addressed. Necessary and sufficient conditions for the asymptotic stability of the systems are established. It is shown that: 1) the asymptotic stability of discrete-time systems depends only on the modules of the eigenvalues of matrix Ā^k and of the continuous-time systems depends only on phases of the eigenvalues of the matrix A^k, 2) the discrete-time systems are asymptotically stable for all admissible values of the discretization step if and only if the continuous-time systems are asymptotically stable, 3) the upper bound of the discretization step depends on the eigenvalues of the matrix A.

Słowa kluczowe

EN

analysis; comparison; stability; discrete-time; continuous-time; linear system

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2016
• Tom: Vol. 26, no. 4
• Strony: 551--563
• Opis fizyczny: Bibliogr. 12 poz., wzory

Twórcy

autor

Kaczorek T.

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

Bibliografia

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• [2] F. R. Gantmacher: The Theory of Matrices, Chelsea Pub. Comp., London, 1959.
• [3] T. Kaczorek: Approximation of positive stable continuous-time linear systems by positive stable discrete-time systems. Pomiary Automatyka Robotyka, 2 (2013), 359-364.
• [4] T. Kaczorek: Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems. Int. J. of Applied Mathematics and Computer Science, 23(3), (2013), 501-506.
• [5] T. Kaczorek: Comparison of approximation methods of positive stable continuous-time linear systems by positive stable discrete-time systems.Archives of Electrical Engineering, 62(2), (2013), 345-355.
• [6] T. Kaczorek: Influence of the value of discretization step on the stability of positive and fractional systems. Proc. National Conf. on Automation, Wroclaw, Poland, (2014), 1-8.
• [7] T. Kaczorek: Inverse systems of linear systems. Archives of Electrical Engineering, 59(3-4), (2010), 203-216.
• [8] T. Kaczorek: Linear Control Systems, vol. 1. Research Studies Press, J. Wiley, New York, 1992.
• [9] T. Kaczorek: Vectors and Matrices in Automation and Electrotechnics. WNT, Warszawa, 1998 (in Polish).
• [10] T. Kailathh: Linear Systems. Prentice-Hall, Englewood Cliffs, New York, 1980.
• [11] H. Rosenbrock: State-Space and Multivariable Theory. J. Wiley, New York, 1970.
• [12] S. H. Żak: Systems and Control. Oxford University Press, New York, 2003.