Structured H∞H∞-optimal control for nested interconnections: A state-space solution

If imposing general structural constraints on controllers, it is unknown how to design optimal H∞H∞-controllers by convex optimization. Under the so-called quadratic invariance condition on 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 block-triangular structure of the standard plant’s control channel and of the controller fall into this class. Recently it has been shown how to design optimal H2H2-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∞H∞-synthesis problem without any counterpart in the literature. We argue that a solution based on Riccati equations is–even for state-feedback synthesis–not feasible and we illustrate our results by means of a simple numerical example.