Multi-ℌ∞ controller design and illustration on an overhead crane

While reliable and efficient tools are widely available to solve (full-order) ℌ_∞ control problems, formulating appropriate weighting functions constitutes the main obstacle to a good ℌ_∞ controller design. In order to facilitate the weighting function design, we propose to break apart the classical ℌ_∞ objective into various ℌ_∞ design objectives and constraints, each relating to a particular closed-loop subsystem. The result is a versatile and intuitive control design approach, and the resulting control problem is solved using the Lyapunov shaping paradigm. The potential of our approach is demonstrated on an overhead crane setup.