The model-matching problem in locally convex space (Q2752605)

The author studies a model-matching problem in a special locally convex topological space, that is, find \(\hat{Q} \in VRH_{\infty}\) minimizing the following cost functional: NEWLINE\[NEWLINE J(\hat{Q})=\min_{Q} J(Q)=\|T_1 (\cdot,\xi)-T_2(\cdot,\xi)QT_3(\cdot,\xi)\|_{\infty}, NEWLINE\]NEWLINE where \(T_1(\cdot,\xi), T_2(\cdot,\xi), T_3(\cdot,\xi) \in VHR_{\infty}\) are given, \(\xi\in \mathbb{R}^n\) is a parameter, and \(VHR_{\infty}\) is the function space of bounded holomorphic rational functions on the right-half plane. She proves that there exists a solution to the above problem, which is an extension of the result for the same problem in the case without any parameter.