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