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Robust Control of Descriptor Systems

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Author(s) : Philip Losse , Volker Mehrmann , Lisa Katrin Poppe , Timo Reis

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 47-2007

MSC 2000

93B36 $^\infty$-control
34A09 Implicit equations, differential-algebraic equations

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.

Keywords : descriptor system, $\mathcal{H}_\infty$-control, algebraic Riccati equation, even matrix pencil, deflating subspace