Stability of continuous-time linear systems described by state equation with fractional commensurate orders of derivatives;Stabilność ciąglych ukladów liniowych opisanych równaniem stanu o wspólmiernych niecalkowitych rzędach pochodnych

Przeglad Elektrotechniczny

Volumn 88, Issue 4 B, 2012, Pages 17-20

  Busłowicz, Mikołaj ^a  

^a BIALYSTOK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Ciagly; Kryterium Michajlowa; Niecalkowitego rzedu; Stabilno ; Uklad liniowy

Indexed keywords

EID: 84859336063     PISSN: 00332097     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (28)

1. Das S., Functional Fractional Calculus for System Identification and Controls. Springer, Berlin 2008.
2. Kilbas A. A., Srivastava H. M. Trujillo J. J. Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006.
3. Ostalczyk P., Epitome of the Fractional Calculus, Theory and its Applications in Automatics, Publishing Department of Technical University of Łódź, Łódź 2008 (in Polish).
4. Podlubny I., Fractional Differential Equations, Academic Press, San Diego 1999.
5. Sabatier. J., Agrawal O. P., Machado J. A. T. (Eds), Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering, Springer, London 2007.
6. Debnath L., Recent applications of fractional calculus to science and engineering, International Journal of Mathematics and Mathematical Sciences, 54 (2003), 3413-3442, http://ijmms.hindawi.com.
7. Calderon A. J., Vinagre B. M., Feliu V., Fractional order control strategies for power electronic buck converters, Signal Processing, 86 (2006), 2803-2819.
8. Pommier V., Sabatier J., Lanuse P., Oustaloup A., Crone control of nonlinear hydraulic actuator, Control Enginnering Practice, 10 (2002), 391-402.
9. Petras I., Stability of fractional-order systems with rational orders: a survey, Fractional Calculus & Applied Analysis. An International Journal for Theory and Applications, 12 (2009), 269-298.
10. Radwan A. G., Soliman A. M., Elwakil A. S., Sedeek A., On the stability of linear systems with fractional-order elements, Chaos, Solitons and Fractals, 40 (2009), 2317-2328.
11. Busłowicz M., Frequency domain method for stability analysis of linear continuous-time fractional systems. In: Malinowski K., Rutkowski L. (Eds.): Recent Advances in Control and Automation, Academic Publishing House EXIT, Warsaw 2008, 83-92.
12. Busłowicz M., Stability analysis of linear continuous-time fractional systems of commensurate order, Journal of Automation, Mobile Robotics and Intelligent Systems, 3 (2009), 16-21.
13. Busłowicz M., Stability of linear continuous-time fractional order systems with delays of the retarded type, Bull. Pol. Acad. Sci., Tech. Sci., 56, (2008), 319-324.
14. Busłowicz M., Stability of state-space models of linear continuous-time fractional order systems, Acta Mechanica et Automatica, 5 (2011), 15-22.
15. Gałkowski K., Bachelier O., Kummert A., Fractional polynomial and nD systems a continuous case, Proc. of IEEE Conf. on Decision & Control, 2006, San Diego, USA.
16. Sabatier J., Moze M., Farges C., LMI stability conditions for fractional order systems, Computers and Mathematics with Applications, 59 (2010), 1594-1609.
17. Tavazoei M. S., Haeri M., Note on the stability of fractional order systems, Mathematics and Computers in Simulation, 79 (2009), 1566-1576.
18. Deng W, Li C., Lu J., Stability analysis of linear fractional differential systems with multiple time delays, Nonlinear Dynamics, 48 (2007), 409-416.
19. Busłowicz M., Computer method for stability analysis of linear discrete-time systems of fractional commensurate order, Przegla{ogonek}d Elektrotechniczny, 86 (2010), 112-115 (in Polish).
20. Dzieliński A., Sierociuk D., Stability of discrete fractional statespace systems, Proc. of 2nd IFAC Workshop on Fractional Differentiation and its Applications (IFAC FDA'06), 2006, 518-523.
21. Gałkowski K., Fractional polynomial and nD systems, Proc. of IEEE Symposium on Circuits and Systems (ISCAS-2005), 2005, Kobe, Japan.
22. Kaczorek T., Fractional positive linear systems and electrical circuits, Przegla{ogonek}d Elektrotechniczny, 84 (2008), 135-141.
23. Kaczorek T., Positivity and reachability of fractional electrical circuits, Acta Mechanica et Automatica, 5 (2011), 42-51.
24. Kaczorek T., Necessary and sufficient stability conditions of fractional positive continuous-time linear systems, Acta Mechanica et Automatica, 5 (2011), 52-54.
25. Kaczorek T., Positive linear systems consisting of n subsystems with different fractional orders, IEEE Trans. Circuits and Systems-I: Regular papers, vol. 58, No. 7, 2011.
26. Kaczorek T., Selected Problems of Fractional Systems Theory, Publishing Department of Białystok University of Technology, Białystok 2009 (in Polish).
27. Kaczorek T., Selected Problems of Fractional Systems Theory, Springer, Berlin 2011.
28. Keel L. H. and Bhattacharyya S. P., A generalization of Mikhailov's criterion with applications, Proc. of the American Control Conference, Chicago, USA, 6 (2000), 4311-4315.