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

Abstract

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.

17 pages

Cited by in corpus (3)

• Convex Structured Controller Design
• Localized LQR Optimal Control
• Distributed Control Subject to Delays Satisfying an ${\mathcal{H}}_{\infty }$ Norm Bound