Interpolation by Rational Matrix Functions and Stability of Feedback Systems: The 4-Block Case

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 a 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 ∞ 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 ∞-control problem is equivalent to the prescribed interpolation problem.

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