Comparison between two set membership methods for frequency domain system identification using fractional models

The main objective of this paper is to estimate the whole set of feasible parameters of a fractional differentiation model, through two methods based on complex frequency data. The first one uses a rectangular inclusion function with rectangle sides corresponding to real and imaginary parts of the complex frequency response; whereas the second one uses a polar inclusion function and the magnitude/phase representation. Each inclusion function introduces some pessimism differently. It is shown that the two approaches are complementary and that the results can be merged to obtain the smallest feasible solution set.