TitlePositive electrical circuits with the chain structure and cyclic Metzler state matrices
Journal titleBulletin of the Polish Academy of Sciences: Technical Sciences
AffiliationKaczorek, Tadeusz : Bialystok University of Technology, Faculty of Electrical Engineering, Wiejska 45D, 15-351 Białystok, Poland
Keywordscyclic matrix ; positive ; electrical circuit ; fractional ; Metzler matrix
Divisions of PASNauki Techniczne
- A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. Philadelphia: SIAM, 1994.
- L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications. New York: J. Wiley, 2000.
- T. Kaczorek, Positive 1D and 2D Systems. London: Springer-Verlag, 2002.
- T. Kaczorek, “Positive linear systems with different fractional orders,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 58, no. 3, pp. 453–458, 2010.
- T. Kaczorek, “Normal fractional positive linear systems and electrical circuits,” in Proc. Conf. Automation 2019, Warsaw, 2020, pp. 13–26.
- T. Kaczorek, Selected Problems of Fractional Systems Theory. Berlin: Springer, 2011.
- T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits. Cham: Springer, 2015.
- W. Mitkowski, “Dynamical properties of metzler systems,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 54, no. 4, pp. 309–312, 2008.
- W. Mitkowski, Outline of Control Theory. Kraków: Publishing House AGH, 2019.
- P. Ostalczyk, Discrete Fractional Calculus. River Edge, NJ: World Scientific, 2016.
- I. Podlubny, Fractional Differential Equations. San Diego: Academic Press, 1999.
- T. Kaczorek, “Reachability and observability of positive discrete-time linear systems with integer positive and negative powers of the state frobenius matrices,” Arch. Control Sci., vol. 28, no. 1, pp. 5–20, 2018.
- M.D. Ortigueira and J. A. Tenreiro Machado, “New discrete-time fractional derivatives based on the bilinear transformation: definitions and properties,” J. Adv. Res., vol. 25, pp. 1–10, 2020.
- A. Ruszewski, “Stability of discrete-time fractional linear systems with delays,” Arch. Control Sci., vol. 29, no. 3, pp. 549–567, 2019.
- L. Sajewski, “Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 65, no. 5, pp. 709–714, 2017.
- R. Stanisławski, K. Latawiec, and M. Łukaniszyn, “A comparative analysis of laguerre-based approximatiors to the grunwald-letnikov fractional-order difference,” Math. Probl. Eng., vol. 2015, 2015.
- F.G. Gantmacher, The Theory of Matrices. London: Chelsea Pub. Comp., 1959.
- T. Kaczorek and K. Borawski, “Stability of continuoustime and discrete-time linear systems with inverse state matrices,” Meas. Autom. Monit., vol. 62, no. 4, pp. 132–135, 2016.
- T. Kaczorek, Polynomial and Rational Matrices. London: Springer, 2007.