Discretization of complex-order differintegrals

Barbosa, Ramiro; Tenreiro Machado, J. A.; Silva, Manuel

http://hdl.handle.net/10400.22/13259

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Authors

Barbosa, Ramiro

Tenreiro Machado, J. A.

Silva, Manuel

Abstract(s)

This paper deals with the discretization of integrals and derivatives (i.e., differintegrals) of complex order. Several methods for the discretization of the operator s􀁊, where y = u+jv is a complex value, are proposed. The concept of conjugated-order differintegral is also presented. The conjugated-order operator allows the use of complexorder differintegrals while still resulting in real time responses and real transfer functions. The performance of the resulting approximations is evaluated both in the time and frequency domains.

Keywords

Fractional calculus Fractional-order systems Complex-order differintegrals Conjugated-order differintegrals IIR filters Discretization Rational approximations CFE method Fractional-order control