Ball, Joseph A.; Rakowski, Marek Interpolation by rational matrix functions and stability of feedback systems: The 4-block case. (English) Zbl 0793.47011 Ando, T. (ed.) et al., Operator theory and complex analysis. Proceedings of a workshop, held in Sapporo, Japan, June 11-14, 1991. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 59, 96-142 (1992). Summary: We consider the problem of constructing rational matrix functions which satisfy a set of finite order directional interpolation conditions on the left and right, as well as collection of infinite order directional interpolation conditions on both sides. We set down consistency requirements for solutions to exist as well as a normalization procedure to make the conditions independent, and show how the general standard problem of \(H^ \infty\) control fits into this framework. We also solve an inverse problem: given an admissible set of interpolation conditions, we characterize the collection of plants for which the associated \(H^ \infty\)-control problem is equivalent to the prescribed interpolation problem.For the entire collection see [Zbl 0782.00047]. Cited in 6 Documents MSC: 47A57 Linear operator methods in interpolation, moment and extension problems 47A56 Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) 93B52 Feedback control 93B36 \(H^\infty\)-control Keywords:lumped and generic interpolation; homogeneous interpolation problem; stabilizing compensators; 4-block problem; \(H^ \infty\) control; rational matrix functions; interpolation conditions PDFBibTeX XMLCite \textit{J. A. Ball} and \textit{M. Rakowski}, in: Operator theory and complex analysis. Proceedings of a workshop, held in Sapporo, Japan, June 11-14, 1991. Basel: Birkhäuser. 96--142 (1992; Zbl 0793.47011)