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A Subspace Framework for ${\mathcal H}_\infty$-Norm Minimization by Aliyev, Nicat; Benner, Peter; Mengi, Emre; Voigt, Matthias is a scholarly article available to read on EtoBox.

What is A Subspace Framework for ${\mathcal H}_\infty$-Norm Minimization about?

We deal with the minimization of the ${\mathcal H}_\infty$-norm of the transfer function of a parameter-dependent 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 interpolatory approaches inspired by our recent work [Aliyev et al., SIAM J. Matrix Anal. Appl., 38(4):1496--1516, 2017] for the computation of the ${\mathcal H}_\infty$-norm. In this work, we minimize the ${\mathcal H}_\infty$-norm of a reduced-order parameter-dependent system obtained by two-sided restrictions onto certain subspaces. Then we expand the subspaces so that Hermite interpolation properties hold between the full and reduced-order system at the optimal parameter value for the reduced order system. We formally establish the superlinear convergence of the subspace frameworks under some smoothness assumptions. The fast convergence of the proposed frameworks in practice is illustrated by several large-scale systems.

Author

Aliyev, Nicat; Benner, Peter; Mengi, Emre; Voigt, Matthias

Published

2019

Language

EN