Barbosa, Ramiro S.Machado, J. A. TenreiroSilva, Manuel F.2014-06-252014-06-2520081077-54631741-2986http://hdl.handle.net/10400.22/4590In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.engFractional calculusDiscretizationComplex-order differintegralsConjugated-order differintegralsFractional-order controljournal article10.1177/1077546307087445