H∞ control design with D-unstable weighting filters and a D-stability constraint: Solution and applications

This paper proposes a new approach for solving a weighted-sensitivity ${{\mathcal{H}}_\infty }$ control problem with a closed-loop ${\mathcal{D}}$-stability requirement. Our method allows for the use of ${\mathcal{D}}$-unstable weighting filters in the controller design, which results in convenient problem formulations for certain types of robust control problems. We show how it can be implemented by straightforwardly extending well-known LMI-based formulations and nonsmooth formulations, and provide a freely available software package to facilitate its practical usage. The effectiveness of our method is experimentally demonstrated on a simple mechatronic setup.