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Lookup NU author(s): Professor Jim Agler, Dr Zinaida LykovaORCiD, Professor Nicholas Young
We analyse a special case of the robust stabilization problem under structured uncertainty. We obtain a new criterion for the solvability of the spectral Nevanlinna-Pick problem, which is a special case of the $\mu$-synthesis problem of $H^\infty$ control in which $\mu$ is the spectral radius. Given $n$ distinct points $\la_1,\dots,\la_n$ in the unit disc and $2\times 2$ nonscalar complex matrices $W_1,\dots,W_n$, the problem is to determine whether there is an analytic $2\times 2$ matrix function $F$ on the disc such that $F(\la_j)=W_j$ for each $j$ and the supremum of the spectral radius of $F(\la)$ is less than 1 for $\la$ in the disc. The condition is that the minimum of a quadratic function of pairs of positive $3n$-square matrices subject to certain linear matrix inequalities in the data be attained and be zero.
Author(s): Agler J, Lykova ZA, Young NJ
Publication type: Article
Publication status: Published
Journal: SIAM Journal on Control and Optimization
Year: 2013
Volume: 51
Issue: 3
Pages: 2472-2508
Date deposited: 21/03/2013
ISSN (print): 0363-0129
ISSN (electronic): 1095-7138
Publisher: SIAM Publications
URL: http://dx.doi.org/10.1137/120873248
DOI: 10.1137/120873248
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