On the essential instabilities caused by fractional-order transfer functions

Mathematical Problems in Engineering

Volumn 2008, Issue , 2008, Pages

  Merrikh Bayat, Farshad ^a   Karimi Ghartemani, Masoud ^a  

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

[No Author keywords available]

Indexed keywords

POLES; PROBABILITY DENSITY FUNCTION; SYSTEM STABILITY;

BRANCH POINTS; CHARACTERISTIC EQUATIONS; ILLUSTRATIVE EXAMPLES; STABILITY CONDITIONS;

TRANSFER FUNCTIONS;

EID: 57249116194     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2008/419046     Document Type: Article

References (20)

1. Mossaheb S., A Nyquist type stability criterion for linear multivariable delayed systems International Journal of Control 1980 32 5 821 847
2. Krall A. M., On the Michailov criterion for exponential polynomials SIAM Review 1966 8 184 187
3. King-Smith E. A., Stability analysis of linear continuous time-delay feedback systems International Journal of Control 1971 13 4 633 655
4. Curtain R. F., Zwart H. J., An Introduction to Infinite-Dimensional Linear Systems Theory 1995 21 Berlin, Germany Springer Texts in Applied Mathematics
5. Matignon D., Stability properties for generalized fractional differential systems Systmes Diffrentiels Fractionnaires 1998 5 Paris, France Society for Industrial and Applied Mathematics 145 158 ESAIM Proceedings
6. Haddar H., Hlie T., Matignon D., A Webster-Lokshin model for waves with viscothermal losses and impedance boundary conditions: strong solutions Proceedings of the 6th International Conference on Mathematical and Numerical Aspects of Wave Propagation Phenomena (WAVES 03) June-July 2003 Jyvskyl, Finland 66 71
7. Ray S. S., Poddar B. P., Bera R. K., Analytical solution of a dynamic system containing fractional derivative of order one-half by a domian decomposition method Journal of Applied Mechanics 2005 72 2 290 295
8. Podlubny I., Fractional Differential Equations 1999 198 San Diego, Calif, USA Academic Press xxiv+340 Mathematics in Science and Engineering
9. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications 1993 Yverdon, Switzerland Gordon and Breach Science xxxvi+976
10. Ahn H.-S., Chen Y. Q., Podlubny I., Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality Applied Mathematics and Computation 2007 187 1 27 34
11. Chen Y. Q., Ahn H. S., Xue D., Robust controllability of interval fractional order linear time invariant systems Signal Processing 2006 86 10 2794 2802
12. Karmarkar J. S., Stability analysis of systems with distributed delay Proceedings of IEE 1970 117 7 1425 1429
13. Pich R., Graphical feedback stability criterion for undamped continuous elastic systems Structural Control 1987 Dordrecht, The Netherlands Nijhoff 532 549
14. Jury E. I., Zaheb E., On a stability test for a class of distributed system with delays IEEE Transactions on Circuits and Systems 1977 37 10 1027 1028
15. Ikeda M., Takahashi S., Generalization of Rouths algorithm and stability criterion for non-integer integral system Electronics and Communications in Japan 1977 60 2 41 50
16. Hwang C., Cheng Y.-C., A numerical algorithm for stability testing of fractional delay systems Automatica 2006 42 5 825 831
17. LePage W. R., Complex Variables and the Laplace Transform for Engineers 1961 New York, NY, USA McGraw-Hill xvii+475 International Series in Pure and Applied Mathematics
18. Cohn H., Conformal Mapping on Riemann Surfaces 1967 New York, NY, USA McGraw-Hill xiv+325
19. Gross B., Braga E. P., Singularities of Linear System Functions 1961 New York, NY, USA Elsevier viii+90
20. Oppenheim A. V., Willsky A. S., Hamid Nawab S., Signals and Systems 1996 Upper Saddle River, NJ, USA Prentice Hall