  If imposing general structural constraints on controllers, it is unknown how
to design $H_\infty$-controllers by convex optimization. Under a so-called
quadratic invariance structure of the generalized plant, the Youla
parametrization allows to translate the structured synthesis problem into an
infinite-dimensional convex program. Nested interconnections that are
characterized by a standard plant with a block-triangular structure fall into
this class. Recently it has been shown how to design optimal $H_2$-controllers
for such nested structures in the state-space by solving algebraic Riccati
equations. In the present paper we provide a state-space solution of the
corresponding output-feedback $H_\infty$ synthesis problem without any
counterpart in the literature. We argue that a solution based on Riccati
equations is - even for state-feedback problems - not feasible and we
illustrate our results by means of a simple numerical example.
