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Reachability of standard and fractional continuous-time systems with constant inputs

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Języki publikacji
EN
Abstrakty
EN
The reachability of standard and fractional-order continuous-time systems with constant inputs is addressed. Positive and non-positive continuous-time linear systems are considered. Necessary and sufficient conditions for the existence of such constant inputs that steers the system from zero initial conditions to the given final state in desired time are derived and proved. As an example of such systems the electrical circuits with DC voltage sources are presented
Rocznik
Strony
147--159
Opis fizyczny
Bibliogr. 24 poz., schem., wykr., wzory
Twórcy
autor
  • Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Bialystok, Poland
Bibliografia
  • [1] O. P. Agrawal, J. A. Tenreiro-Machado and I. Sabatier: Fractional Derivatives and Their Applications, volume 38 of Nonlinear Dynamics. Springer- Verlag, Berlin, 2004.
  • [2] P. Antsaklis and A. N. Michel: Linear Systems. Birkhäuser, Boston, 2006.
  • [3] D. Balenau, Z. B. Günvenc and J. A. Tenreiro-Machado: New Trends in Nanotechnology and Fractional Calculus Applications. Springer, 2010.
  • [4] M. Buslowicz and T. Kaczorek: Reachability and minimum energy control of positive linear discrete-time systems with multiple delays in state and control. Measurement Automation and Monitoring, 53(10), (2007), 40-44.
  • [5] L. Farina and S. Rinaldi: Positive Linear Systems: Theory and Applications. J. Wiley & Sons, New York, 2000.
  • [6] F. R. Gantmacher: The Theory of Matrices, volume I and II. Chelsea Publishing Co., New York, 1959. Translated by K. A. Hirsch.
  • [7] R. Hilfer: Applications of Fractional Calculus in Physics. World Scientific, Singapore, 2000.
  • [8] T. Kaczorek: Linear Control Systems: Analysis of Multivariable Systems. Research Studies Press, New York, 1992.
  • [9] T. Kaczorek: Vectors and Matrices in Automation and Electrotechnics. Scientific and Technical Publishing, WNT, Warsaw, 1998.
  • [10] T. Kaczorek: Positive 1D and 2D systems. Communications and control engineering. Springer-Verlag, London, 2002.
  • [11] T. Kaczorek: Positive electrical circuits and their reachability. Archives of Electrical Engineering, 60(3), (2011), 283-301.
  • [12] T. Kaczorek: Positivity and reachability of fractional electrical circuits. Acta Mechanica et Automatica, 5(2), (2011), 45-51.
  • [13] T. Kaczorek: Selected Problems of Fractional Systems Theory. Springer-Verlag, Berlin, 2011.
  • [14] T. Kaczorek: Reachability and observability of fractional positive electrical circuits. Computational Problems of Electrical Engineering, 3(2), (2014), 28-36.
  • [15] T. Kaczorek and K. Rogowski: Reachability of linear hybrid systems described by the general model. Archives of Control Sciences, 20(2), (2010), 199-207.
  • [16] T. Kaczorek and K. Rogowski: Fractional Linear Systems and Electrical Circuits. Springer-Verlag, Berlin, 2015.
  • [17] T. Kailath: Linear Systems. Prentice-Hall, Engelwood Cliffs, New York, 1980.
  • [18] R. L. Magin: Fractional Calculus in Bioengineering. Begell House Publisher, Rodding, 2006.
  • [19] K. B. Oldham and J. Spanier: The Fractional Calculus. Academic Press, New York, 1974.
  • [20] I. Podlubny: Fractional Differential Equations. Academic Press, San Diego, 1994.
  • [21] L. Sajewski: Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders. Multidimensional Systems and Signal Processing, (2014), 1-15.
  • [22] L. Sajewski: Reachability of fractional positive continuous-time linear systems with two different fractional orders. In Recent Advances in Automation, Robotics and Measuring Techniques, volume 267 pages 239-249, 2014.
  • [23] W. Trzasko: Reachability and controllability of positive fractional-order discrete-time systems. Measurements Automation Robotics, 17(2), (2013), 365-370.
  • [24] M. E. Valcher: Reachability analysis for different classes of positive systems. In R. Bru and S. Romero-Vivo, editors, Positive Systems, volume 389 of Lecture Notes in Control and Information Sciences, pages 29-41. Springer Berlin Heidelberg, 2009.
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę
Typ dokumentu
Bibliografia
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