Introduction to fractional linear systems. Part 1: continuous-time case

IEE Proceedings: Vision, Image and Signal Processing

Volumn 147, Issue 1, 2000, Pages 62-70

  Ortigueira, M D ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FRACTALS; FREQUENCY RESPONSE; LAPLACE TRANSFORMS; LINEAR SYSTEMS; STEP RESPONSE; TRANSFER FUNCTIONS;

CONTINUOUS TIME LINEAR SYSTEMS; FRACTIONAL DIFFERENTIAL EQUATIONS; STATIONARY FRACTAL;

SIGNAL PROCESSING;

EID: 0033872505     PISSN: 1350245X     EISSN: None     Source Type: Journal    
DOI: 10.1049/ip-vis:20000272     Document Type: Article

References (27)

1. KALIA, R.N.: Recent advances in fractional calculus' (Global Publishing Company, 1993)
2. MILLER, K.S., and ROSS, B.: An introduction to the fractional calculus and fractional differential equations' (Wiley, 1993)
3. SAMKO, S.O., KILBAS, A.A., and MARICHEV, O.I.: Fractional integrals and derivatives-theory and applications' (Gordon and Breach Science Publishers, 1987)
4. CAMPOS, L.M.C.: On a concept of derivative of complex order with applications to special functions', IMA J. Appl. Math., 1984, 33, pp. 109-133
5. CAMPOS, L.M.C.: On the solution of some simple fractional differential equations', Int. J. Math. Math. Sci., 1990, 13, (3), pp. 481-496
6. NISHIMOTO, K.: Fractional calculus' (Descartes Press Co., Koriyama, Japan, 1989)
7. KOH, C.G., and KELLY, J.M.: Application of fractional derivatives to seismic analysis of based-isolated models', Earthq. Eng. Struct. Dyn., 1990, 19, pp. 229-241
8. MANDELBROT, B.B.: The fractal geometry of nature' (W. H. Freeman and Company, New York, 1983)
9. MANDELBROT, B.B., and VAN NESS, J.W.: The fractional Brownian motions, fractional noises and applications', SIAM Re\, 1968, 10, pp. 4
10. ANASTASIO, T.J.: The fractional-order dynamics of brainstem vestibulo-oculomotor neurons', Biol. Cybern., 1994, 72, pp. 69-79
11. GAUL, L., KLEIN, P., and KEMPLE, S.: Damping description involving fractional operators', Mech. Syst. Signal Process., 1991, 5, (2), pp. 81-88
12. MAKRIS, H, and CONSTANTINOU, M.C.: Fractional-derivative Maxwell model for viscous dampers', J. Struct Eng., 1991, 117, (9), pp. 2708-2724
13. CLERC, J.P., TREMBLAY, A.-M.S., ALBINET, G., and MITESCU, C.D.: a. c. response of fractal networks', J. Phys. Lett., 1984, 45, (1), pp. 913-924
14. KESHNER, M.S.: M/f Noise', Proc. IEEE, 1982, 70, pp. 212-218
15. VAN DER ZIEL, A.: Unified presentation of 1/f noise in electronic devices: fundamental 1/f noise sources', Pmc. IEEE, 1988, 76, pp. 233258
16. OUSTALOUP, A.: Fractional order sinusoidal oscillators: optimization and their use in highly linear FM modulation', IEEE Trans. Circuits Syst., 198I, CAS-28, pp. 10
17. MACHADO, J.A.T.: Analysis and design of fractional-order digital control systems', SAMS, 1997, 27, pp. 107-122
18. MATIGNON, D., D'ANDRÉA-NOVEL, B.: Décomposition modale fractionaire de 1' équation des ondes avec pertes viscothermiques'. Tech. Rep. 95 C 001, École Nationale Supérieure des Télécommunications, France, 1995
19. OUSTALOUP, A., MATHIEU, B., and LANUSSE, P.: The CRONE control of resonant plants: application to a flexible transmission', Eur. J. Control, 1995, 1, pp. 113-121
20. MACHADO, J.A.T., and AZENHA, A.: Position/force fractional control of mechanical manipulators'. Proceedings of 1998 5th Int. Workshop on Advanced Motion Control, Coimbra, Portugal, pp. 216221
21. FENANDER, A.: Modal synthesis when modeling damping by use of fractional derivatives', AIAA J., 1996, 34, (5), pp. 1051-1058
22. KOELLER, R.C.: Polynomial operators, Stieltjes convolution, and fractional calculus in hereditary mechanics', Ada Mech., 1986, 58, pp. 251-264
23. LIEBST, B.S., and TORVIK, P.J.: Asymptotic approximations for systems incorporating fractional derivative damping', J. Dyn. Syst. Meas. Control, 1996, 118, pp. 572-579
24. ORTIGUEIRA, M.D.: Introduction to fractional signal processing', INESC Internal Report, 1997
25. HENRICI, P.: Applied and computational complex analysis, II, (Wiley, 1977)
26. REED, I.S., LEE, P.C., and TRUONG, T.K.: Spectral representation of fractional Brownian motion in n dimensions and its properties', IEEE Trans. Inf. Ttieory, 1995, 41, (5), pp. 1439-1451
27. DECARLO, R.-A.: Linear systems: a state variable approach with numerical implementation' (Prentice-Hall, Englewood ClifTs, USA, 1989)