An efficient numerical algorithm for stability testing of fractional-delay systems

ISA Transactions

Volumn 48, Issue 1, 2009, Pages 32-37

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

^a SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Fractional delay equation; Fractional order system; Numerical algorithm; Stability analysis

Indexed keywords

COMPUTER APPLICATIONS; NATURAL SCIENCES;

CHARACTERISTIC EQUATION; CHARACTERISTIC FUNCTIONS; FRACTIONAL DELAY; FRACTIONAL-ORDER SYSTEMS; MULTIVALUED FUNCTIONS; NUMERICAL ALGORITHMS; STABILITY ANALYSIS; STABILITY TESTING;

SYSTEM STABILITY;

EID: 57549092045     PISSN: 00190578     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.isatra.2008.10.003     Document Type: Article

References (14)

1. Chen C.F., and Chiu R.F. Evaluation of irrational and transcendental transfer functions via the fast fourier transform. International Journal of Electronics 35 (1973) 267-276
2. Curtain R.F., and Zwart H.J. An introduction to infinite-dimensional linear systems thoery. Text in applied mathematics vol. 21 (1995), Springer, Berlin
3. LePage W.R. Complex variables and the Laplace transform for engineers (1961), McGraw-Hill
4. Matignon D. Stability properties for generalized fractional differential systems, In: ESAIM: Proc. 5, 1998, p. 145-58
5. Ozturk N., and Uraz A. An analytic stability test for a certain class of distributed parameter systems with a distributed lag. IEEE Transactions on Automatic Control 29 4 (1984) 368-370
6. Ozturk N., and Uraz A. An analytic stability test for a certain class of distributed parameter systems with delay. IEEE Transactions on CAS 32 4 (1985) 393-396
7. Hotzel R. Some stability conditions for fractional delay systems. Journal of Mathematical Systems, Estimation, and Control 8 4 (1998) 1-19
8. Chen Y.Q., and Moore K.L. Analytical stability bound for a class of delayed fractional-order dynamical systems. Nonlinear Dynamics 29 1-4 (2002) 191-200
9. Hwang C., and Cheng Y.-C. A numerical algorithm for stability testing of fractional delay systems. Automatica 42 (2006) 825-831
10. Bonnet C., and Partington J.R. Stabilization of fractional exponential systems including delays. Kybernetika (Prague) 37 3 (2001) 345-353
11. Bonnet C., and Partington J.R. Analysis of fractional delay systems of retarded and neutral type. Automatica 38 7 (2002) 1133-1138
12. Corless R.M., Gonnet G.H., Hare D.E.G., Jeffrey D.J., and Knuth D.E. On the Lambert W function. Advances in Computational Mathematics 5 (1996) 329-359
13. Bogacki P., and Shampine L.F. A 3(2) pair of Runge-Kutta formulas. Applied Mathematics Letters 2 (1989) 1-9
14. μ-controllers, In: Proc. of the 36th IEEE CDC, 1999