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\(\mathcal{L}_{\infty}\)-norm computation for large-scale descriptor systems using structured iterative eigensolvers. (English) Zbl 1405.93028
Summary: In this article, we discuss a method for computing the \(\mathcal{L}_\infty\)-norm for transfer functions of descriptor systems using structured iterative eigensolvers. In particular, the algorithm computes some desired imaginary eigenvalues of an even matrix pencil and uses them to determine an upper and lower bound to the \(\mathcal{L}_\infty\)-norm. Finally, we compare our method to a previously developed algorithm using pseudopole sets. Numerical examples demonstrate the reliability and accuracy of the new method along with a significant drop in the runtime.

MSC:
93A15 Large-scale systems
93B40 Computational methods in systems theory (MSC2010)
15A22 Matrix pencils
93-04 Software, source code, etc. for problems pertaining to systems and control theory
93C05 Linear systems in control theory
93B55 Pole and zero placement problems
93B60 Eigenvalue problems
93C15 Control/observation systems governed by ordinary differential equations
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