A note on the stability of fractional order systems

Mathematics and Computers in Simulation

Volumn 79, Issue 5, 2009, Pages 1566-1576

  Tavazoei, Mohammad Saleh ^a   Haeri, Mohammad ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fractional order LTI system; Interval systems; Robust stability; Stability

Indexed keywords

CONTROL THEORY; INVARIANCE; LINEAR SYSTEMS; STABILITY;

DO-MAINS; FRACTIONAL ORDER LTI SYSTEM; FRACTIONAL ORDERS; INTERVAL SYSTEMS; LINEAR TIME INVARIANT SYSTEMS; NEW APPROACHES; ROBUST STABILITY; ROBUST STABILITY CHECKS; STABILITY ANALYSES; STABILITY PROPERTIES;

SYSTEM STABILITY;

EID: 57649105528     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2008.07.003     Document Type: Article

References (18)

1. Anderson B.D.O., Bose N.K., and Jury E.I. A simple test for zeros of a complex polynomial in a sector. IEEE Trans. Automat. Control 19 (A1974) 437-438
2. Chen Y.Q., Ahn H., and Podlubny I. Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Process. 86 (2006) 2611-2618
3. Davison E.J., and Ramesh N. A note on the eigenvalues of a real matrix. IEEE Trans. Automat. Control 15 April (1970) 252-253
4. Delgado-Romero J.J.D., Gonzalez-Garza R.S., Hernandez-Morales E., and Delgado-Romero G. Robust stability of linear time invariant systems represented by an interval matrix. 1st International Conference in Control of Oscillations and Chaos, Proceedings, 3 August 27-29 (1997) 545-548
5. Hostetter G.H. An improved test for the zeros of a polynomial in a sector. IEEE Trans. Automat. Control 20 (1975) 433-434
6. Hwang C., and Cheng Y.C. A numerical algorithm for stability testing of fractional delay systems. Automatica 42 (2006) 825-831
7. B.J. Lurie, Tunable TID controller, US patent 5,371,670, December 6, 1994.
8. Matignon D. Stability results for fractional differential equations with applications to control processing. Computational Engineering in Systems Applications. Lille, France, IMACS, IEEE-SMC, vol. 2, July (1996) 963-968
9. Matignon D. Stability properties for generalized fractional differential systems. ESAIM: Proc. 5 (1998) 145-158
10. Ostalczyk P. Nyquist characteristics of a fractional order integrator. J. Fract. Calculus 19 (2001) 67-78
11. Oustaloup A., Levron F., Mathieu B., and Nanot F.M. Frequency-band complex non-integer differentiator: Characterization and synthesis. IEEE Trans. Circuits Syst. I: Fundam. Theory Appl. 47 1 (2000) 25-39
12. Oustaloup A., Moreau X., and Nouillant M. The CRONE suspension. Control Eng. Pract. 4 8 (1996) 1101-1108
13. Petras I., Chen Y.Q., and Vinagre B.M. Robust stability test for interval fractional order linear systems. In: Blondel V.D., and Megretski A. (Eds). Unsolved Problems in the Mathematics of Systems and Control (2004), Princeton University Press, Princeton, NJ 208-210 (Chapter 6.5)
14. Petras I., Chen Y.Q., Vinagre B.M., and Podlubny I. Stability of linear time invariant systems with interval fractional orders and interval coefficients. Proceedings of the International Conference on Computation Cybernetics (ICCC04). Vienna Technical University, Vienna, Austria (2005) 1-4
15. μ-controllers. IEEE Trans. Automat. Control 44 1 (1999) 208-214
16. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
17. Qiu Z., Muller P.C., and Frommer A. Ellipsoidal set-theoretic approach for stability of linear state-space models with interval uncertainty. Math. Comput. Simul. 57 (2001) 45-59
18. Raynaud H.F., and ZergaInoh A. State-space representation for fractional order controllers. Automatica 36 (2000) 1017-1021