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If imposing general structural constraints on controllers, it is unknown howto design $H_\infty$-controllers by convex optimization. Under a so-calledquadratic invariance structure of the generalized plant, the Youlaparametrization allows to translate the structured synthesis problem into aninfinite-dimensional convex program. Nested interconnections that arecharacterized by a standard plant with a block-triangular structure fall intothis class. Recently it has been shown how to design optimal $H_2$-controllersfor such nested structures in the state-space by solving algebraic Riccatiequations. In the present paper we provide a state-space solution of thecorresponding output-feedback $H_\infty$ synthesis problem without anycounterpart in the literature. We argue that a solution based on Riccatiequations is - even for state-feedback problems - not feasible and weillustrate our results by means of a simple numerical example.

Structured $H_\infty$-Optimal Control for Nested Interconnections: A State-Space Solution