Directional interpolation in the state space (Q1104898)

The author considers the standard \(H^{\infty}\) optimization problem. Given \(T_ 1\), \(T_ 2\) rational matrix functions whose entries are in \(H^{\infty}\), characterize all \(\Phi\) of this class for which \(T_ 2^{-1}(T_ 1-\Phi)\) is such a function and such that \(\| \Phi \|_{\infty}<1\). The author presents a new state space characterization of the well-known parametrized solution to this problem.