Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders

Bulletin of the Polish Academy of Sciences: Technical Sciences

Volumn 60, Issue 2, 2012, Pages 279-284

  Buslowicz M ^a  

^a BIALYSTOK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Continuous time; Fractional; Linear system; Mikhailov criterion; Stability

Indexed keywords

ASYMPTOTIC STABILITY; CONVERGENCE OF NUMERICAL METHODS; EQUATIONS OF STATE; LINEAR SYSTEMS; STABILITY; STABILITY CRITERIA; SYSTEM STABILITY;

ARGUMENT PRINCIPLES; CONTINUOUS-TIME; CONTINUOUS-TIME LINEAR SYSTEMS; FRACTIONAL; MIKHAILOV CRITERION; STABILITY ANALYSIS; STABILITY PROBLEM; STABILITY THEORIES;

CONTINUOUS TIME SYSTEMS;

EID: 84989344359     PISSN: 02397528     EISSN: None     Source Type: Journal    
DOI: 10.2478/v10175-012-0037-2     Document Type: Article

References (26)

1. S. Das, Functional Fractional Calculus for System Identification and Controls, Springer, Berlin, 2008.
2. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
3. P. Ostalczyk, Epitome of the Fractional Calculus, Theory and its Applications in Automatics, Publishing Department of Technical University of Łódź, Łódź, 2008, (in Polish).
4. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
5. J. Sabatier., O.P. Agrawal, and J.A.T. Machado, Advances in Fractional Calculus, Theoretical Developments and Applications in Physics and Engineering, Springer, London, 2007.
6. L. Debnath, "Recent applications of fractional calculus to science and engineering", Int. J. Mathematics and Mathematical Sciences 54, 3413-3442 (2003), http://ijmms.hindawi.com.
7. I. Petras, "Stability of fractional-order systems with rational orders: a survey", Fractional Calculus & Applied Analysis. Int. J. Theory and Applications 12, 269-298 (2009).
8. A.G. Radwan, A.M. Soliman, A.S. Elwakil, and A. Sedeek, "On the stability of linear systems with fractional-order elements", Chaos, Solitons and Fractals 40, 2317-2328 (2009).
9. M. Busłowicz, "Frequency domain method for stability analysis of linear continuous-time fractional systems", in: Recent Advances in Control and Automation, eds. K. Malinowski and L. Rutkowski, pp. 83-92, Academic Publishing House EXIT, Warsaw, 2008.
10. M. Busłowicz, "Stability analysis of linear continuous-time fractional systems of commensurate order", J. Automation, Mobile Robotics and Intelligent Systems 3, 16-21 (2009).
11. M. Busłowicz, "Stability of linear continuous-time fractional order systems with delays of the retarded type", Bull. Pol. Ac.: Tech. 56, 319-324 (2008).
12. M. Busłowicz, "Stability of state-space models of linear continuous-time fractional order systems", Acta Mechanica et Automatica 5, 15-22 (2011).
13. M. Busłowicz, "Stability of continuous-time linear systems described by state equation with fractional commensurate orders of derivatives", Proc. SENE, Electrical Review 88, 17-20 (2012).
14. K. Gałkowski, O. Bachelier, and A. Kummert, "Fractional polynomial and nD systems a continuous case", Proc. IEEE Conf. on Decision & Control 1, CD-ROM (2006).
15. J. Sabatier, M. Moze, and C. Farges, "LMI stability conditions for fractional order systems", Computers and Mathematics with Applications 59, 1594-1609 (2010).
16. M.S. Tavazoei, and M. Haeri, "Note on the stability of fractional order systems", Mathematics and Computers in Simulation 79, 1566-1576 (2009).
17. W. Deng, C. Li, and J. Lu, "Stability analysis of linear fractional differential systems with multiple time delays", Nonlinear Dynamics 48, 409-416 (2007).
18. M. Busłowicz, "Computer method for stability analysis of linear discrete-time systems of fractional commensurate order", Electrical Review 86, 112-115 (2010), (in Polish).
19. A. Dzieliński, and D. Sierociuk, "Stability of discrete fractional state-space systems", Proc. 2nd IFAC Workshop on Fractional Differentiation and its Applications 1, 518-523 (2006).
20. K. Gałkowski and A. Kummert, "Fractional polynomial and nD systems", Proc. IEEE Symposium on Circuits and Systems, ISCAS' 2005 1, CD-ROM (2005).
21. M. Busłowicz, "Robust stability of positive discrete-time linear systems of fractional order", Bull. Pol. Ac.: Tech. 58, 567-572 (2010).
22. T. Kaczorek, "Positivity and reachability of fractional electrical circuits", Acta Mechanica et Automatica 5, 42-51 (2011).
23. T. Kaczorek, "Necessary and sufficient stability conditions of fractional positive continuous-time linear systems", Acta Mechanica et Automatica 5, 52-54 (2011).
24. T. Kaczorek, "Positive linear systems consisting of n subsystems with different fractional orders", IEEE Trans. Circuits and Systems - I: Regular papers 58 (7), 1203-1210 (2011).
25. T. Kaczorek, "Positive fractional 2D continuous-discrete linear systems", Bull. Pol. Ac.: Tech. 59, 575-579 (2011).
26. T. Kaczorek T., Selected Problems of Fractional Systems Theory, Springer, Berlin, 2011.