Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
The transfer matrix of the standard and fractional linear discrete-time linear systems is investigated. Necessary and sufficient conditions for zeroing of the transfer matrix of the linear discrete-time systems are established. The considerations are illustrated by examples of the standard and fractional linear discrete-time systems.
Czasopismo
Rocznik
Tom
Strony
188--191
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
autor
- Faculty of Electrical Engineering, Bialystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
autor
- Faculty of Electrical Engineering, Bialystok University of Technology, ul. Wiejska 45D, 15-351 Białystok, Poland
Bibliografia
- 1. Abu-Saris R, Al-Mdallal Q. On the asymptotic stability of linear sys-tem of fractional-order difference equations. Fract. Calc. Appl. Anal. 2013; 16: 613-629.
- 2. Antsaklis E, Michel A. Linear Systems. Birkhauser, Boston, 2006.
- 3. Cermak J, Gyori I, Nechvatal L. On explicit stability conditions for a linear fractional difference system. Fract. Calc. Appl. Anal. 2015; 18: 651-672.
- 4. Dörfler F, Coulson J, Markovsky I. Bridging direct & indirect data-driven control formulations via regularizations and relaxations. Trans. Automat. Contr., 2023.
- 5. Farina L, Rinaldi S. Positive Linear Systems: Theory and Applica-tions. J. Wiley & Sons, New York, 2000.
- 6. Goodrich C, Peterson A. Discrete Fractional Calculus. Springer, Cham, 2015.
- 7. Kaczorek T. Positivity and reachability of fractional electrical circuits. Acta Mechanica et Automatica. 2011; 5(2): 42-51.
- 8. Kaczorek T. Positive linear systems consisting of n subsystems with different fractional orders. IEEE Trans. Circuits and Systems. 2011; 58(6): 1203-1210.
- 9. Kaczorek T. Selected Problems of Fractional Systems Theory. Berlin, Germany: Springer-Verlag, 2011.
- 10. Kaczorek T. Normal positive electrical circuits. IET Control Theory Appl. 2015; 9(5): 691–699.
- 11. Kaczorek T, Rogowski K. Fractional Linear Systems and Electrical Circuits. Studies in Systems, Decision and Control, Vol. 13, Springer, 2015.
- 12. Kailath T. Linear systems. Prentice Hall, Englewood Cliffs, New York, 1980.
- 13. Kalman R. Mathematical description of linear systems. SIAM J. Control. 1963; 1(2): 152-192.
- 14. Kalman R. On the general theory of control systems. Proc. First Intern. Congress on Automatic Control. London, UK: Butterworth, 1960; 481-493.
- 15. Klamka J. Controllability of Dynamical Systems. Kluwer, Dordrecht, Netherlands, 1981.
- 16. Markovsky I, Dörfler F. Behavioral systems theory in data-driven analysis, signal processing, and control. Annual Reviews in Control. 2021; 52: 42–64.
- 17. Mozyrska D, Wyrwas M. The Z-transform method and delta type fractional difference operators. Discrete Dyn. Nat. Soc. 2015; (2-3): 1-12.
- 18. Oldham K, Spanier J. The fractional calculus: integrations and differ-entiations of arbitrary order. New York, USA: Academic Press, 1974.
- 19. Ostalczyk P. Discrete Fractional Calculus: Applications in Control and Image Processing; Series in Computer Vision, World Scientific Publishing, Hackensack, New York, 2016.
- 20. Podlubny I. Fractional differential equations. San Diego, USA: Aca-demic Press, 1999.
- 21. Poldermann JW, Willems J.C. Introduction to Mathematical Systems Theory. Texts in Applied Mathematics, vol. 26. Springer, New York, NY, 1998.
- 22. Rosenbrock H. State-space and multivariable theory. New York, USA: J. Wiley, 1970.
- 23. Ruszewski A. Stability of discrete-time fractional linear systems with delays, Archives of Control Sciences. 2019; 29(3): 549-567.
- 24. Sabatier J, Agrawal OP, Machado JAT. Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering. Springer, London, 2007.
- 25. Sajewski Ł. Stabilization of positive descriptor fractional discrete-time linear systems with two different fractional orders by decentralized controller. Bull. Pol. Acad. Sci. Techn. 2017; 65(5): 709-714.
- 26. Song TT, Wu GC, Wei JL. Hadamard fractional calculus on time scales, Fractals. 2022; 30(7), 2250145.
- 27. Sun HG, Zhang Y, Baleanu D, Chen W, Chen YQ. A new collection of real world applications of fractional calculus in science and engi-neering. Commun. Nonlinear Sci. Numer. Simul. 2018; 64: 213-231.
- 28. Wu GC, Abdeljawad T, Liu J, Baleanu D, Wu KT. Mittag-Leffler stability analysis of fractional discrete-time neural networks via fixed point technique. Nonlinear Analysis: Model. Contr. 2019; 24: 919-936.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-dc98a7af-f6e0-4ecb-970b-74af9b162671