Robust Control of Descriptor Systems

Abstract

The $\mathcal{H}_\infty$ control problem is studied for linear constant coefficient descriptor systems. Necessary and sufficient optimality conditions are derived in terms of deflating subspaces of even matrix pencils for index one systems as well as for higher index problems. It is shown that this approach leads to a more robust method in computing the optimal value $\gamma$ in contrast to other methods such as the widely used Riccati based approach. The results are illustrated by a numerical example.