Have a personal or library account? Click to login
Pointwise Completeness and Pointwise Degeneracy of Descriptor Linear Discrete-Time Systems with Different Fractional Orders Cover

Pointwise Completeness and Pointwise Degeneracy of Descriptor Linear Discrete-Time Systems with Different Fractional Orders

Open Access
|Jun 2025

References

  1. Busłowicz M. Stability analysis of continuous-time linear systems consisting of n subsystem with different fractional orders. Bull. Pol. Ac.: Tech. 2012; 60(2): 279-284.
  2. Campbell SL, Meyer CD and Rose NJ. Applications of the Drazin inverse to linear systems of differential equations with singular constant coefficients. SIAMJ Appl. Math. 1976; 31(3): 411-425.
  3. Dai L. Singular control systems. Lectures Notes in Control and Information Sciences. Springer-Verlag. Berlin; 1989.
  4. Dzieliński A, Sierociuk D, Sarwas G. Ultracapacitor parameters identification based on fractional order model. Proc ECC. Budapest; 2009.
  5. Fahmy MM, O’Reill J. Matrix pencil of closed-loop descriptor systems: infinite-eigenvalues assignment, Int. J. Control. 1989; 49(4): 1421-1431.
  6. Ferreira NMF, Machado JAT. Fractional-order hybrid control of robotic manipulators, Proc. 11th Int. Conf. Advanced Robotics. ICAR Coimbra. Portugal; 2003: 393-398.
  7. Guang-Ren D. Analysis and Design of Descriptor Linear Systems. Springer. New York; 2010.
  8. Kaczorek T. Pointwise Completeness and Pointwise Degeneracy of Linear Systems. In: Selected Problems of Fractional Systems Theory. Lecture Notes in Control and Information Sciences. Springer, Berlin Heidelberg. 2011;411: 81-101.
  9. Kaczorek T. Pointwise completeness and pointwise degeneracy of fractional descriptor continuous-time linear systems with regular pencils, Bulletin of the Polish Academy of Sciences Technical Sciences. 2015;63(1): 169-172, 2015.
  10. Kaczorek, T. Positive linear systems with different fractional orders. Bull. Pol. Ac.: Tech. 2010;58(3): 453-458.
  11. Kaczorek, T. Selected Problems in Fractional Systems Theory. Springer-Verlag. Berlin; 2011.
  12. Kaczorek T, Busłowicz M. Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems. Journal of Automation. Mobile Robotics and Intelligent Systems. 2009; 3(1): 8-11.
  13. Kaczorek T, Rogowski K. Fractional Linear Systems and Electrical Circuits. Springer; 2015.
  14. Kaczorek T, Sajewski Ł. The pointwise completeness and the pointwise degeneracy of linear discrete-time different fractional orders systems, Bulletin of the Polish Academy of Sciences: Technical Sciences. 2020; 68 (6); 1513-1516.
  15. Kaczorek T, Sajewski Ł. Pointwise completeness and the pointwise degeneracy of fractional standard and descriptor linear continuoustime systems with different fractional, International Journal of Applied Mathematics & Computer Science. 2020; 30(4).
  16. Korobov AA. On pointwise degenerate linear delay-differential systems with nonnilpotent passive matrices, J. Appl. Industr. Math. 2017; 11(3): 369–380.
  17. Kucera V, Zagalak P. Fundamental theorem of state feedback for singular systems. Automatica. 1988; 24 (5): 653-658.
  18. Kundel P, Mehrmann V. Differential algebraic equations. Analysis and numerical solution 2nd edition. EMS Textboobs in Mathematics. Berlin; 2024.
  19. Metel'skii AV, Karpuk VV. On properties of pointwise degenerate linear autonomous control systems. I. Autom. Remote Control. 2009; 70(10): 1613–1625.
  20. Kundel P, Mehrmann V. Differential–algebraic equations. Analysis and numerical solution 2nd edition. EMS Textbooks in Mathematics. Berlin Mathematical Society (EMS); 2024.
  21. Liu Ma W, Wei Y. Multilinear time-invariant descriptor system. Computational and Applied Mathematics; 2025.
  22. Weia IY, Liu W, Wei C. T-Jordan canonical form and T-Drazin inverse based on the T-product. Commun.Appl.Math.Comput. 2021; 3(2):201-220.
  23. Miao Y, Qi Y. Wei, T-Jordan canonical form and T-Drazin inverse based on the T-product. Commun. Appl. Math. Comput. 2021; 3(2):201-220.
  24. Miller KS, Ross B. An Introduction to the Fractional Calculus and Fractional Differenctial Equations. Willey New York; 1993.
  25. Podlubny I, Fractional Differential Equations. Academic Press. San Diego;1999.
  26. Sajewski Ł. Reachability, observability and minimum energy control of fractional positive continuous-time linear systems with two different fractional orders. Multidim. Syst. Sign. Process. 25.
  27. Sajewski Ł. Minimum energy control of fractional positive continuoustime linear systems with two different fractional orders and bounded inputs, Advances in Modelling and Control of Non-integer-Order Systems. Lecture Notes in Electrical Engineering. 2015; 320:171-181.
  28. Trzasko W. Pointwise Completeness and Pointwise Degeneracy of Linear Continuous-Time Systems with Different Fractional Orders. In: Szewczyk R, Zieliński C, Kaliczyńska M. (eds) Recent Advances in Automation. Robotics and Measuring Techniques. Advances in Intelligent Systems and Computing. Springer Cham. 2014; 267: 307-316.
  29. Wei Y, Stanimirovic P. Petkovic M. Numerical and symbolic computations of generalized inverses. Hackensack NJ World Scientific; 2018.
DOI: https://doi.org/10.2478/ama-2025-0035 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 288 - 291
Submitted on: Jul 13, 2024
Accepted on: Jun 6, 2025
Published on: Jun 26, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Tadeusz KACZOREK, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.