The general distance problem inH∞optimal control theory

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Abstract
The general distance problem that arises in H∞ optimal control theory is considered. Transformations that reduce the general H∞ problem to the general distance problem are reviewed, and an iterative scheme called γ-iteration is considered, in which the general distance problem is reduced to a standard best approximation problem. The γ-iteration is viewed as a problem of finding the zero crossing of a function, This function is shown to be continuous, monotonically decreasing, convex and bounded by some very simple functions. These properties make it possible to obtain very rapid convergence of the iterative process. The issues of model-reduction and approximation in H∞-synthesis will also be addressed.