Relationship between the observability of standard and fractional linear systems

• Autorzy: Kaczorek T.

Identyfikatory

DOI

10.1515/acsc-2017-0027

• Języki publikacji: EN

Abstrakty

EN

The relationship between the observability of standard and fractional discrete-time and continuous-time linear systems are addressed. It is shown that the fractional discrete-time and continuous-time linear systems are observable if and only if the standard discrete-time and continuous-time linear systems are observable.

Słowa kluczowe

EN

fractional; standard; linear; discrete-time; continuous-time; system; observability

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2017
• Tom: Vol. 27, no. 3
• Strony: 441--451
• Opis fizyczny: Bibliogr. 25, wzory

Twórcy

autor

Kaczorek T.

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

Bibliografia

• [1] P. Antsaklis and A. Michel: Linear Systems. Birkhauser, Boston, 2006.
• [2] L. Farina and S. Rinaldi: Positive Linear Systems: Theory and Applications. J. Wiley & Sons, New York, 2000.
• [3] F. R . Gantmacher: The Theory of Matrices. Chelsea Pub. Comp., London, 1959.
• [4] T. Kaczorek: Constructability and observability of standard and positive electrical circuits. Electrical Review, 89(7) (2013), 132-136.
• [5] T. Kaczorek: Controllability and observability of linear electrical circuits Electrical Review, 87(9a) (2011), 248-254.
• [6] T. Kaczorek: Linear Control Systems. Vol. 1, J. Wiley, New York, 1999.
• [7] T. Kaczorek: Positive 1D and 2D Systems. Springer-Verlag, London, 2002.
• [8] T. Kaczorek: Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems, 58(6) (2011), 1203-1210.
• [9] T. Kaczorek: Reachability and controllability to zero tests for standard and positive fractional discrete-time systems. Journal Européen des Systemes Automatisés, JESA, 42(6-8) (2008), 769-787.
• [10] T. Kaczorek: Reachability and observability of fractional positive electrical circuits. Computational Problems of Electrical Engineering, 23(2) (2013), 28-36.
• [11] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, 2011.
• [12] T. Kaczorek: Vectors and Matrices in Automation and Electrotechnics. WNT, Warsaw, 1998, (in Polish).
• [13] T. Kailath: Linear Systems. Prentice Hall, Englewood Cliffs, New Yok, 1980.
• [14] R. Kalman: Mathematical description of linear systems. SIAM J. Control, 1(2) (1963), 152-192.
• [15] R. Kalman: On the general theory of control systems. Prof. First Int. Congress on Automatic Control, Butterworth, London, (1960), 481-493.
• [16] J. Klamka: Controllability of Dynamical Systems. Kluwer, Academic Press, Dordrecht, 1991.
• [17] J. lamka: Relationship between controllability of standard and fractional linear systems. Submitted to KKA, Krakow, (2017).
• [18] K. Oldham and J. Spanier: The Fractional Calculus: Integrations and Differentiations of Arbitrary Order. Academic Press, New York, 1974.
• [19] P. Ostalczyk: Epitome of the Fractional Calculus, Theory and its Applications in Automatics. Technical University of Lodz Press, Lodz, 2008 (in Polish).
• [20] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1999.
• [21] H. Rosenbrock: State-space and Multivariable Theory. J. Wiley, New York, 1970.
• [22] Ł. Sajewski: Reachability of fractional positive continuous-time linear systems with two different fractional orders. In: Recent Advances in Automation, Robotics and Measuring Techniques, Series in Advances in Intelligent Systems and Computing, 267 (2014), 239-249.
• [23] Ł. Sajewski: Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders. Multidimensional Systems and Signal Processing, 27(1), (2016), 27-41.
• [24] W. Wolovich: Linear Multivariable Systems. Springer-Verlag, New York, 1974.
• [25] S. H. Żak: Systems and Control. Oxford University Press, New York, 2003.

Uwagi

EN

The studies have been carried out in the framework of work No. S/WE/1/2016 and financed from the funds for science by the Polish Ministry of Science and Higher Education

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).