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The generalization of the ν-gap metric to a finitely connected stability region is derived. The results hold for the class of all linear, time-invariant systems which admit a continuous coprime factorization including the nonrational case. A limited extension of the H∞-loopshaping synthesis procedure is obtained via conformal mapping. An example is given where enlargement of the stability region can be used to transform the problem into one which is solvable via uniform stability margin optimization.