Title

Positivity and cyclicity of descriptor electrical circuits with chain structure

Journal title

Bulletin of the Polish Academy of Sciences Technical Sciences

Yearbook

2022

Volume

70

Issue

1

Authors

Kaczorek, Tadeusz ; Borawski, Kamil

Affiliation

Kaczorek, Tadeusz : Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok, Poland ; Borawski, Kamil : Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, 15-351 Białystok, Poland

Keywords

cyclic matrix ; descriptor ; positive ; electrical circuit ; fractional ; Metzler matrix

Divisions of PAS

Nauki Techniczne

Coverage

e139955

Bibliography

1.  A. Berman and R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. Philadelphia: SIAM, 1994.
2.  L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications. New York: J. Wiley, 2000.
3.  T. Kaczorek, Positive 1D and 2D Systems. London: Springer-Verlag, 2002.
4.  T. Kaczorek, “Positive linear systems with different fractional orders,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 58, no. 3, pp. 453– 458, 2010.
5.  T. Kaczorek, Selected Problems of Fractional Systems Theory. Berlin: Springer, 2011.
6.  T. Kaczorek, “Normal fractional positive linear systems and electrical circuits,” in Proc. Conf. Automation 2019, Warsaw, 2020, pp. 13–26.
7.  T. Kaczorek and K. Rogowski, Fractional Linear Systems and Electrical Circuits. Cham: Springer, 2015.
8.  W. Mitkowski, “Dynamical properties of Metzler systems,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 54, no. 4, pp. 309–312, 2008.
9.  W. Mitkowski, Outline of Control Theory. Kraków: Publishing House AGH, 2019.
10.  P. Ostalczyk, Discrete Fractional Calculus. River Edge, NJ: World Scientific, 2016.
11.  I. Podlubny, Fractional Differential Equations. San Diego: Academic Press, 1999.
12.  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.
13.  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.
14.  A. Ruszewski, “Stability of discrete-time fractional linear systems with delays,” Arch. Control Sci., vol. 29, no. 3, pp. 549– 567, 2019.
15.  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.
16.  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, p. 512104, 2015.
17.  L. Dai, Singular Control Systems, ser. Lecture Notes in Control and Information Sciences. Berlin: Springer, 1989, vol. 118.
18.  D. Guang-Ren, Analysis and Design of Descriptor Linear Systems. New York: Springer, 2010.
19.  T. Kaczorek, Linear Control Systems. vol. 1. New York, USA: J. Wiley, 1992.
20.  T. Kaczorek and K. Borawski, Descriptor Systems of Integer and Fractional Orders, ser. Studies in Systems, Decision and Control. Cham: Springer, 2021, vol. 367.
21.  K. Borawski, “Superstabilization of Descriptor ContinuousTime Linear Systems via State-Feedback Using Drazin Inverse Matrix Method,” Symmetry, vol. 12, no. 6, p. 940, 2020.
22.  M. Rami and D. Napp, “Characterization and Stability of Autonomous Positive Descriptor Systems,” IEEE Trans. Autom. Contr., vol. 57, no. 10, pp. 2668–2673, 2012.
23.  E. Virnik, “Stability analysis of positive descriptor systems,” Linear Algebra Appl., vol. 429, no. 10, pp. 2640–2659, 2008.
24.  F.G. Gantmacher, The Theory of Matrices. London: Chelsea Pub. Comp., 1959.
25.  T. Kaczorek, “Positive electrical circuits with the chain structure and cyclic Metzler state matrices,” Bull. Pol. Acad. Sci. Tech. Sci., vol. 69, no. 4, pp. 1–5, 2021.

Date

25.02.2022

Type

Article

Identifier

DOI: 10.24425/bpasts.2021.139955