We are concerned with the computation of the L∞-norm for an L∞-function of the form H(s) = C(s)D(s) −1 B(s), where the middle factor is the inverse of a meromorphic matrix-valued function, and C(s), B(s) are meromorphic functions mapping to shortand-fat and tall-and-skinny matrices, respectively. For instance, transfer functions of descriptor systems and delay systems fall into this family. We focus on the case where the middle factor is large-scale. We propose a subspace projection method to obtain approximations of the function H where the middle factor is of much smaller dimension. The L∞-norms are computed for the resulting reduced functions, then the subspaces are refined by means of the optimal points on the imaginary axis where the L∞-norm of the reduced function is attained. The subspace method is designed so that certain Hermite interpolation properties hold between the largest singular values of the original and reduced functions. This leads to a locally superlinearly convergent algorithm with respect to the subspace dimension, which we prove and illustrate on various numerical examples.

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We deal with the minimization of the H∞-norm of the transfer function of a parameterdependent descriptor system over the set of admissible parameter values. Subspace frameworks are proposed for such minimization problems where the involved systems are of large order. The proposed algorithms are greedy interpolatary approaches inspired by our recent work [

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