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Journal Article

Faster and More Accurate Computation of the H∞ Norm via Optimization

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Benner,  Peter
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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Mitchell,  Tim
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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Citation

Benner, P., & Mitchell, T. (2018). Faster and More Accurate Computation of the H∞ Norm via Optimization. SIAM Journal on Scientific Computing, 40(5), A3609-A3635. doi:10.1137/17M1137966.


Cite as: https://hdl.handle.net/21.11116/0000-0000-2E61-0
Abstract
In this paper, we propose an improved method for computing the
$\mathcal{H}_\infty$ norm of linear dynamical systems that results in a code
that is often several times faster than existing methods. Our approach uses
standard optimization tools to rebalance the work load of the standard
algorithm due to Boyd, Balakrishnan, Bruinsma, and Steinbuch, with the aim of
minimizing the number of expensive eigenvalue computations that must be
performed. Unlike the standard algorithm, our improved approach can also
calculate the $\mathcal{H}_\infty$ norm to full precision with little extra
work, and also offers some opportunity to improve its performance via
parallelization. Finally, our improved method is also applicable for
approximating the $\mathcal{H}_\infty$ norm of large-scale systems.