A graphical test for the interval stability of fractional-delay systems

Computers and Mathematics with Applications

Volumn 62, Issue 3, 2011, Pages 1501-1509

  Yu, Y J ^a,b   Wang, Z H ^a,c  

^a NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

^b CHANGZHOU UNIVERSITY   (China)

^c PLA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Edge theorem; Fractional delay systems; Graphical test; Robust stability

Indexed keywords

BIBO STABILITY; BOUNDED INPUT; EDGE THEOREM; FRACTIONAL-DELAY SYSTEMS; FREQUENCY RESPONSE PLOTS; GRAPHICAL TEST; POLYTOPES; ROBUST STABILITY; STABILITY TESTING;

CONTROL SYSTEM ANALYSIS; FREQUENCY RESPONSE;

SYSTEM STABILITY;

EID: 79960994806     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.03.067     Document Type: Article

References (18)

1. C.A. Monje, Y.-Q. Chen, B.M. Vinagre, D.-Y. Xue, and V. Feliu Fractional-Order Systems and Controls: Fundamentals and Applications 2010 Springer-Verlag London
2. N. Heyman Fractional calculus description of non-linear viscoelastic behavior of ploymers Nonlinear Dynamics 38 2004 221 231
3. D. Ingman, and J. Suzdalnitsky Application of dynamic fractional differentiation to the study of oscillating viscoelastic medium with cylindrical cavity ASME Journal of Vibration and Acoustics 124 2002 642 645
4. K. Adolfsson Nonlinear fractional order viscoelasticity at large strains Nonlinear Dynamics 38 2004 233 246 (Pubitemid 40400618)
5. C. Hwang, and Y.C. Cheng A numerical algorithm for stability testing of fractional delay systems Automatica 42 2006 825 831
6. S.E. Hamamci An algorithm for stabilization of fractional order time delay systems using fractional-order PID Controllers IEEE Transactions on Automatic Control 52 2007 1964 1969 (Pubitemid 350130541)
7. A.M. Kamran, and H. Mohammad On robust stability of LTI fractional-order delay systems of retarded and neutral type Automatica 46 2010 362 368
8. D. Matignon Stability results for fractional differential equations with applications to control processing Computational Engineering in Systems Applications vol. 2 1996 IEEE-SMC Lille, France, IMACS 963 968
9. M. Buslowicz Stability of linear continuous-time fractional order systems with delays of the retarded type Bulletin of the Polish Academy of Sciences: Technical Sciences 56 2008 319 324
10. C. Bonnet, and J.R. Partington Analysis of fractional delay systems of retarded and neutral type Automatica 38 2002 1133 1138 (Pubitemid 34524669)
11. C. Bonnet, and J.R. Partington Stabilization of some fractional delay systems of retarded and neutral type Automatica 43 2007 2047 2053 (Pubitemid 350148069)
12. Z.H. Wang, and H.Y. Hu Stability of a linear oscillator with damping force of fractional order derivative Science China: Physics, Mechanics and Astronomy 53 2010 345 352
13. M. Shi, Z.H. Wang, An effective analytical criterion for stability testing of fractional-delay systems, Automatica (in press).
14. H. Chapellat, and S.P. Bhattacharyya A generalization of Kharitonov's theorem: robust stability of interval plants IEEE Transactions on Automatic Control 34 1989 306 311
15. Y.Q. Chen, and I. Podlubny Robust stability check of fractional order linear time invariant systems with interval uncertainties Signal Processing 86 2006 2611 2618 (Pubitemid 44026624)
16. V.L. Kharitonov Asymptotic stability of an equilibrium position of a family of systems of linear differential equation Differential Equations 14 1979 1483 1485
17. M.Y. Fu, A.W. Olbrot, and M.P. Polis Robust stability for time-delay systems: the edge theorem and graphical tests IEEE Transactions on Automatic Control 34 1989 813 820
18. N. Tan,.F. zgven, and M.M. zyetkin Robust stability analysis of fractional order interval polynomials ISA Transactions 48 2009 166 172