## Extended and improved criss-cross algorithms for computing the spectral value set abscissa and radius.(English)Zbl 1457.93066

In this paper, the authors extend the original criss-cross algorithms for computing the $$\varepsilon$$-pseudospectral abscissa and radius to general spectral value sets. By proposing new root-finding-based strategies for the horizontal/radial search subphases, authors significantly reduce the number of expensive Hamiltonian eigenvalue decompositions incurred, which typically translates to meaningful speedups in overall computation times. Furthermore, and partly necessitated by our root-finding approach, authors develop a new way of handling the singular pencils or problematic interior searches that can arise when computing the $$\varepsilon$$-spectral value set radius. Compared to would-be direct extensions of the original algorithms, that is, without this additional modifications, their improved criss-cross algorithms are not only noticeably faster but also more robust and numerically accurate, for both spectral value set and pseudospectral problems (From the Summary).

### MSC:

 93D09 Robust stability 93C05 Linear systems in control theory 93B36 $$H^\infty$$-control

### Software:

ARPACK; Eigtool; SLICOT; eigs; PSAPSR; Seigtool
Full Text:

### References:

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