Robust stability for fractional-order systems with structured and unstructured uncertainties

Computers and Mathematics with Applications

Volumn 64, Issue 10, 2012, Pages 3258-3266

  Jiao, Zhuang ^a,b   Zhong, Yisheng ^a  

^a TSINGHUA UNIVERSITY   (China)

^b Utah State University   (United States)

Author keywords

Fractional order system; Norm bounded uncertainty; Polytope type uncertainty; Robust stability

Indexed keywords

FRACTIONAL-ORDER SYSTEMS; NORM-BOUNDED UNCERTAINTY; NUMERICAL EXAMPLE; POLYTOPE-TYPE UNCERTAINTY; ROBUST STABILITY; SOLVING SET; SUFFICIENT AND NECESSARY CONDITION; SUFFICIENT CONDITIONS; UNSTRUCTURED UNCERTAINTY;

ALGORITHMS; MATHEMATICAL MODELS;

LINEAR MATRIX INEQUALITIES;

EID: 84868197753     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2012.03.011     Document Type: Article

References (32)

1. K.B. Oldham, and J. Spanier The Fractional Calculus 1974 Academic Press New York, London
2. A. Oustaloup, B. Mathieu, and P. Lanusse The crone control of resonant plants: application to a flexible transmission European Journal of Control 1 1995 113 121
3. D. Matignon, Stability results on fractional differential equations with applications to control processing, in: Proceedings of the Multiconference on Computational Engineering in Systems and Application, 1996, pp. 963-968.
4. Dμ controllers IEEE Transactions on Automatic Control 44 1999 208 214
5. J.T. Sawicki, and J. Padovan Frequency driven phasic shifting and elastic hysteretic partitioning properties of fractional mechanical system representation schemes Journal of the Franklin Institute 336 1999 423 433
6. H.F. Raynaud, and A. Zergainoh State-space representation for fractional order controllers Automatica 36 2000 1017 1021
7. D.Y. Xue, Y.Q. Chen, A comparative introduction of four fractional order controllers, in: Proceedings of the 4th IEEE World Congress on Intelligent Control and Automation, 2002, pp. 3228-3235.
8. B.M. Vinagre, Y.Q. Chen, and I. Petras Two direct Tustin discretization methods for fractional-order differentiator/integrator Journal of the Franklin Institute 340 2003 349 362
9. C. Hwang, and Y.C. Cheng A numerical algorithm for stability testing of fractional delay systems Automatica 42 2006 825 831
10. B.M. Vinagre, C.A. Monje, A.J. Calderon, and J.I. Suarez Fractional PID controllers for industry application. A brief introduction Journal of Vibration and Control 13 2007 1419 1429 (Pubitemid 47482826)
11. H 2 pseudo-rational approximations to fractional-order linear time invariant systems Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007 61 75
12. Y.Q. Chen, T. Bhaskaran, and D.Y. Xue Practical tuning rule development for fractional order proportional and integral controller Journal of Computational and Nonlinear Dynamics 3 2008 1 8
13. X.J. Wu, J. Li, and G.R. Chen Chaos in the fractional order unified system and its synchronization Journal of the Franklin Institute 345 2008 392 401
14. H.S. Li, Y. Luo, and Y.Q. Chen A fractional order proportional and derivative (fopd) motion controller: tuning rule and experiments IEEE Transactions on Control Systems Technology 18 2009 1 5
15. I. Petras, Y.Q. Chen, B.M. Vinagre, I. Podlubny, Stability of linear time invariant systems with interval fractional orders and interval coefficients, in: Proceedings of the International Conference on Computation Computational Cybernetics, 2004, pp. 341-346. (Pubitemid 40859608)
16. Y.Q. Chen, H.S. Ahn, and I. Podlubny Robust stability check of fractional order linear time invariant systems with interval uncertainties Signal Processing 86 2006 2611 2618 (Pubitemid 44026624)
17. H.S. Ahn, Y.Q. Chen, and I. Podlubny Robust stability test of a class of linear time-invariant interval fractional-order systems using Lyapunov inequality Applied Mathematics and Computation 187 2007 27 34 (Pubitemid 46656399)
18. H.S. Ahn, and Y.Q. Chen Necessary and sufficient stability condition of fractional-order interval linear systems Automatica 44 2008 2985 2988
19. J.G. Lu, and G.R. Chen Robust stability and stabilization of fractional-order interval systems: an LMI approach IEEE Transactions on Automatic Control 54 2009 1294 1299
20. J.G. Lu, and Y.Q. Chen Robust stability and stabilization of fractional-order interval systems with the fractional order α: the 0 < α < 1 case IEEE Transactions on Automatic Control 55 2010 152 158
21. K.A. Moornani, and M. Haeri Robust stability testing function and Kharitonov-like theorem for fractional order interval systems IET Control Theory and Applications 4 2010 2097 2108
22. R.P. Agarwala, V. Lakshmikantham, and J.J. Nieto On the concept of solution for fractional differential equations with uncertainty Nonlinear Analysis, Theory, Methods and Applications 72 2009 2859 2862
23. A.M.A. El-sayed, A.E.M. El-mesiry, and H.A.A. El-saka On the fractional-order logistic equation Applied Mathematics Letters 20 2007 817 823 (Pubitemid 46428071)
24. S.S. Delshad, M.M. Asheghan, and M.H. Beheshti Robust stabilization of fractional-order systems with interval uncertainties via fractional-order controllers Advances in Difference Equations 984601 2010
25. P.P. Khargonekar, I.R. Petersen, and K.M. Zhou Robust stabilization of uncertain linear systems: quadratic stabilizability and control theory IEEE Transactions on Automatic Control 35 1990 356 361
26. T. Mori, and H. Kokame A parameter-dependent Lyapunov function for a polytope of matrices IEEE Transactions on Automatic Control 45 2000 1516 1519
27. J. Sabatier, M. Moze, C. Farges, On stability of fractional order systems, in: Proceeding of 3rd IFAC Workshop on Fractional Differentiation Application, Ankara, Turkey, 2008.
28. B.R. Barmish New Tools for Robustness of Linear Systems 1994 MacMillan New York
29. S. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnan Linear Matrix Inequalities in System and Control Theory 1994 SIAM PA, Philadelphia
30. J.X. Xu, and Z.S. Hou On learning control: the state of the art and perspective Acta Automatica Sinica 31 2005 943 955
31. A. Isidori, L. Marconi, and A. Serrani Robust nonlinear motion control of a helicopter IEEE Transactions on Automatic Control 48 2003 413 426
32. J.C. Willems Least squares stationary optimal control and the algebraic Riccati equation IEEE Transactions on Automatic Control 16 1971 621 634