Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

Discrete Dynamics in Nature and Society

Volumn 2016, Issue , 2016, Pages

  Stanisławski, Rafał ^a   Latawiec, Krzysztof J ^a  

^a OPOLE UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84979670070     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2016/9590687     Document Type: Article

References (37)

1. A. Dubravíc and Z. Sehíc, "Using orthonormal functions in model predictive control, " Tehnicki Vjesnik, vol. 19, no. 3, pp. 513-520, 2012.
2. P. S. C. Heuberger, P. M. J. Van den Hof, and B. Wahlberg, Modeling and Identification with Rational Orthogonal Basis Functions, Springer, London, UK, 2005.
3. B. Ninness, H. Hjalmarsson, and F. Gustafsson, "The fundamental role of general orthonormal bases in system identification, " IEEE Transactions on Automatic Control, vol. 44, no. 7, pp. 1384-1406, 1999.
4. O. Mykhailenko, "Cone crusher model identification using block-oriented systems with orthonormal basis functions, " International Journal of ControlTheory and ComputerModeling, vol. 4, no. 3, pp. 1-8, 2014.
5. A. Wills, T. B. Schön, L. Ljung, and B. Ninness, "Identification of Hammerstein-Wiener models, " Automatica, vol. 49, no. 1, pp. 70-81, 2013.
6. I. Area, J. D. Djida, J. Losada, and J. J. Nieto, "On fractional orthonormal polynomials of a discrete variable, " Discrete Dynamics in Nature and Society, vol. 2015, Article ID 141325, 7 pages, 2015.
7. G. Maione, "On the Laguerre rational approximation to fractional discrete derivative and integral operators, " IEEE Transactions on Automatic Control, vol. 58, no. 6, pp. 1579-1585, 2013.
8. R. Stanisawski, "New Laguerre filter approximators to the Grünwald-Letnikov fractional difference, " Mathematical Problems in Engineering, vol. 2012, Article ID 732917, 21 pages, 2012.
9. R. Stanisawski, K. J. Latawiec, and M. ukaniszyn, "A comparative analysis of Laguerre-based approximators to the Grünwald-Letnikov fractional-order difference, "Mathematical Problems in Engineering, vol. 2015, Article ID 512104, 10 pages, 2015.
10. Y. Q. Chen, I. Petras, and D. Xue, "Fractional order control-a tutorial, " in Proceedings of the American Control Conference (ACC '09), pp. 1397-1411, St. Louis, Mo, USA, June 2009.
11. W. Krajewski and U. Viaro, "A method for the integer-order approximation of fractional-order systems, " Journal of the Franklin Institute, vol. 351, no. 1, pp. 555-564, 2014.
12. B. T. Krishna, "Studies on fractional order differentiators and integrators: A survey, " Signal Processing, vol. 91, no. 3, pp. 386-426, 2011.
13. M. Rachid, B. Maamar, and D. Said, "Comparison between two approximation methods of state space fractional systems, " Signal Processing, vol. 91, no. 3, pp. 461-469, 2011.
14. C. Monje, Y. Chen, B. Vinagre, D. Xue, and V. Feliu, Fractionalorder Systems and Controls: Fundamentals and Applications, Series on Advances in Industrial Control, Springer, London, UK, 2010.
15. D. Mozyrska, "Multiparameter fractional difference linear control systems, "DiscreteDynamics inNature and Society, vol. 2014, Article ID 183782, 8 pages, 2014.
16. I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, Orlando, Fla, USA, 1999.
17. H. Sheng, Y. Q. Chen, and T. S. Qiu, Fractional Processes and Fractional-Order Signal Processing, Springer, New York, NY, USA, 2012.
18. M. Aoun, R. Malti, F. Levron, and A. Oustaloup, "Synthesis of fractional Laguerre basis for system approximation, " Automatica, vol. 43, no. 9, pp. 1640-1648, 2007.
19. R. Stanisawski, K. J. Latawiec, W. P. Hunek, andM. Zukaniszyn, "Laguerre-based modeling of fractional-order LTI SISO systems, " in Proceedings of the 18th International Conference on Methods and Models in Automation and Robotics (MMAR '13), pp. 610-615, Miedzyzdroje, Poland, August 2013.
20. R. Stanisawski and K. J. Latawiec, "Normalized finite fractional differences: computational and accuracy breakthroughs, " International Journal of Applied Mathematics and Computer Science, vol. 22, no. 4, pp. 907-919, 2012.
21. P. Ostalczyk, "Equivalent descriptions of a discrete-time fractional-order linear system and its stability domains, " International Journal of Applied Mathematics and Computer Science, vol. 22, no. 3, pp. 533-538, 2012.
22. D. Mozyrska and M. Wyrwas, "The Z-transform method and delta type fractional difference operators, " Discrete Dynamics in Nature and Society, vol. 2015, Article ID 852734, 12 pages, 2015.
23. S. Guermah, S. Djennoune, and M. Bettayeb, "A new approach for stability analysis of linear discrete-time fractional-order systems, " in New Trends in Nanotechnology and Fractional Calculus Applications, pp. 151-162, Springer, Berlin, Germany, 2010.
24. I. Kheirizad, M. S. Tavazoei, and A. Jalali, "Stability criteria for a class of fractional order systems, " Nonlinear Dynamics, vol. 61, no. 1-2, pp. 153-161, 2010.
25. C. Li and Z. Zhao, "Asymptotical stability analysis of linear fractional differential systems, " Journal of Shanghai University (English Edition), vol. 13, no. 3, pp. 197-206, 2009.
26. I. Petrás, "Stability of fractional-order systems with rational orders: A survey, " Fractional Calculus & Applied Analysis, vol. 12, no. 3, pp. 269-298, 2009.
27. J. Sabatier, M. Moze, and C. Farges, "On stability of fractional order systems, " in Proceedings of the 3rd IFAC Workshop on FractionalDifferentiation and ItsApplications (FDA'08), Ankara, Turkey, November 2008.
28. S. B. Stojanovic and D. L. Debeljkovic, "Simple stability conditions of linear discrete time systems with multiple delay, " Serbian Journal of Electrical Engineering, vol. 7, no. 1, pp. 69-79, 2010.
29. D. Matignon, "Stability results for fractional differential equations with applications to control processing, " in Proceedings of the Computational Engineering in Systems and Applications Multiconference, vol. 2, pp. 963-968, Lille, France, 1996.
30. R. Stanisawski and K. J. Latawiec, "Stability analysis for discrete-time fractional-order LTI statespace systems. Part I: new necessary and sufficient conditions for asymptotic stability, " Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 61, no. 2, pp. 353-361, 2013.
31. R. Stanisawski and K. J. Latawiec, "Stability analysis for discrete-time fractional-order LTI statespace systems. Part II: new stability criterion for FD-based systems, " Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 61, no. 2, pp. 362-370, 2013.
32. C. Boukis, D. P. Mandic, A. G. Constantinides, and L. C. Polymenakos, "A novel algorithm for the adaptation of the pole of Laguerre filters, " IEEE Signal Processing Letters, vol. 13, no. 7, pp. 429-432, 2006.
33. S. T. Oliveira, "Optimal pole conditions for Laguerre and twoparameter Kautz models: A survey of known results, " in Proceedings of the 12th IFAC Symposium on SystemIdentification (SYSID '00), pp. 457-462, Santa Barbara, Calif, June 2000.
34. Q. Chen, W. Mai, L. Zhang, and W. Mi, "System identification by discrete rational atoms, " Automatica, vol. 56, pp. 53-59, 2015.
35. R. Stanisawski, "Identification of open-loop stable linear systems using fractional orthonormal basis functions, " in Proceedings of the 14th International Conference on Methods and Models in Automation and Robotics, pp. 935-985, Miedzyzdroje, Poland, 2009.
36. M. Siami, M. S. Tavazoei, and M. Haeri, "Stability preservation analysis in direct discretization of fractional order transfer functions, " Signal Processing, vol. 91, no. 3, pp. 508-512, 2011.
37. P. M. Van den Hof, P. S. Heuberger, and J. Bokor, "System identification with generalized orthonormal basis functions, " Automatica, vol. 31, no. 12, pp. 1821-1834, 1995.