H∞-control for descriptor systems - A structured matrix pencils approach

The H_∞ 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 problems of arbitrary index. It is shown that this approach leads to a more robust method in computing the optimal value γ in contrast to other methods such as the widely used Riccati or LMI based approaches. The results are illustrated by a numerical example.