Have a personal or library account? Click to login
Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems Cover

Simple Conditions for Practical Stability of Positive Fractional Discrete-Time Linear Systems

Open Access
|Jul 2009

References

  1. Busłowicz, M. (2008a). Stability of linear continuous-time fractional systems of commensurate order, Pomiary, Automatyka, Robotyka: 475-484, (on CD-ROM, in Polish); Journal of Automation, Mobile Robotics and Intelligent Systems 3(1): 16-21.
  2. Busłowicz, M. (2008b). Frequency domain method for stability analysis of linear continuous-time fractional systems, in K. Malinowski and L. Rutkowski (Eds.), Recent Advances in Control and Automation, Academic Publishing House EXIT, Warsaw, pp. 83-92.
  3. Busłowicz, M. (2008c). Robust stability of convex combination of two fractional degree characteristic polynomials, Acta Mechanica et Automatica 2(2): 5-10.
  4. Busłowicz, M. (2008d). Practical robust stability of positive fractional scalar discrete-time systems, Zeszyty Naukowe Politechniki Saląskiej: Automatyka 151: 25-30, (in Polish).
  5. Chen, Y.-Q., Ahn, H.-S. and Podlubny, I. (2006). Robust stability check of fractional order linear time invariant systems with interval uncertainties, Signal Processing 86(10): 2611-2618.10.1016/j.sigpro.2006.02.011
  6. Das, S. (2008). Functional Fractional Calculus for System Identification and Controls, Springer, Berlin.
  7. Dzieliński, A. and Sierociuk, D. (2006). Stability of discrete fractional state-space systems, Proceedings of the 2-nd IFAC Workshop on Fractional Differentiation and Its Applications, IFAC FDA'06, Porto, Portugal, pp. 518-523.
  8. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.10.1002/9781118033029
  9. Gałkowsk, i K. and Kummert, A. (2005). Fractional polynomials and nD systems, Proceedings of the IEEE International Symposium on Circuits and Systems, ISCAS'2005, Kobe, Japan, (on CD-ROM).
  10. Gałkowski, K., Bachelier, O. and Kummert, A. (2006). Fractional polynomial and nD systems—A continuous case, Proceedings ot the IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 2913-2917.
  11. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2
  12. Kaczorek, T. (2007a). Reachability and controllability to zero of positive fractional discrete-time systems, Machine Intelligence and Robotic Control 6(4): 139-143.10.23919/ECC.2007.7068247
  13. Kaczorek, T. (2007b). Reachability and controllability to zero of cone fractional linear systems, Archives of Control Sciences 17(3): 357-367.10.23919/ECC.2007.7068247
  14. Kaczorek, T. (2007c). Choice of the forms of Lyapunov functions for positive 2D Roesser model, International Journal of Applied Mathematics and Computer Science 17(4): 471-475.10.2478/v10006-007-0039-7
  15. Kaczorek, T. (2008a). Fractional positive continuous-time linear systems and their reachability, International Journal of Applied Mathematics and Computer Science 18(2): 223-228.10.2478/v10006-008-0020-0
  16. Kaczorek, T. (2008b). Reachability and controllability to zero tests for standard and positive fractional discrete-time systems, Journal of Automation and System Engineering 42(6-7-8): 769-787.10.3166/jesa.42.769-787
  17. Kaczorek, T. (2008c). Fractional 2D linear systems, Journal of Automation, Mobile Robotics and Intelligent Systems 2(2): 5-9.
  18. Kaczorek, T. (2008d). Positive different orders fractional 2D linear systems, Acta Mechanica et Automatica 2(2): 51-58.
  19. Kaczorek, T. (2008e). Practical stability of positive fractional discrete-time systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 313-317.
  20. Kilbas, A. A., Srivastava, H. M. and Trujillo, J. J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam.
  21. Podlubny, I. (1999). Fractional Differential Equations, Academic Press, San Diego, CA.
  22. Sabatier, J., Agrawal, O. P. and Machado, J. A. T. (Eds.) (2007). Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering, Springer, London.10.1007/978-1-4020-6042-7
  23. Sierociuk, D. (2007). Estimation and Control of Discrete Dynamical Systems of Fractional Order in State Space, Ph.D. thesis, Faculty of Electrical Engineering, Warsaw University of Technology, Warsaw, (in Polish).
  24. Vinagre, B. M., Monje, C. A. and Calderon, A. J. (2002). Fractional order systems and fractional order control actions, Proceedings of the IEEE CDC Conference Tutorial Workshop: Fractional Calculus Applications in Automatic Control and Robotics, Las Vegas, NY, pp. 15-38.
DOI: https://doi.org/10.2478/v10006-009-0022-6 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 263 - 269
Published on: Jul 8, 2009
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2009 Mikołaj Busłowicz, Tadeusz Kaczorek, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 19 (2009): Issue 2 (June 2009)