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Description
We show how to use tangential interpolation techniques to construct structured linearizations for several types of structured rational matrices. The classes studied in this paper are square rational matrices that are either Hermitian, or skew-Hermitian, or complex symmetric, or complex skew-symmetric, upon evaluation on one of the following three curves~: the real axis, the imaginary axis and the unit circle. The proposed linearizations are system matrices for these rational matrices and they preserve the structure of the rational matrices, except for the case of the unit circle. For that case, the rational matrix $R(z)$ is linearized using a palindromic or anti-palindromic system matrix for a modified rational matrix, whose eigenvalues that are not on the unit circle preserve the symmetries of the zeros and poles of $R(z)$. The basic tool used to obtain the results in this paper is tangential interpolation via the Loewner and shifted Loewner matrices. In the case of preserving symmetries with respect to the unit circle, we combine this with Mobius transforms.