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Approximating fractional derivatives in the perspective of system control

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Abstract

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

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Authors and Affiliations

  1. Institute of Engineering of Porto, Department of Electrical Engineering, Rua Dr. Antonio Bernardino de Almeida, 4200-072, Porto, Portugal

    J. A. Tenreiro Machado & Alexandra Galhano

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  1. J. A. Tenreiro Machado
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  2. Alexandra Galhano
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Correspondence to J. A. Tenreiro Machado.

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Machado, J.A.T., Galhano, A. Approximating fractional derivatives in the perspective of system control. Nonlinear Dyn 56, 401–407 (2009). https://doi.org/10.1007/s11071-008-9409-4

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  • DOI: https://doi.org/10.1007/s11071-008-9409-4

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