Directional interpolation approach to H∞-Optimization and robust stabilization

It is shown that, under a mild condition,
H\infty
-optimization and robust stabilization are equivalent to a directional interpolation problem which is a matrix extension of the classical Pick-Nevanlinna interpolation problem. A classical iterative method, which is an extension of the Schur-Nevanlinna algorithm, is given for solving the problem. This method does not require the inner-outer factorization nor the balanced realization of the original plant. A circuit theoretical parameterization of all solutions is derived that is expected to enhance the physical insight to the
H\infty
-optimal control and robust stabilization. This parameterization has the degree much less than the one obtained previously.