Robustness via structured H ∞/H ∞ synthesis

Abstract

Multi-objective H ∞/H ∞-synthesis with structured control laws is discussed and used as a means to enhance robustness of the system in the presence of real parametric uncertainty. NP-hardness of the computation of the structured singular value μ excludes its use within an optimisation procedure and raises the question of how to replace it. We show that the semi-structured distance to instability can be used for that purpose and we indicate how the resulting mixed H ∞ program can be solved efficiently. The method is applied to the regulation of a flexible geostationary satellite.