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## H-infinty-control of discrete-time descriptor systems

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Author(s) : Lisa Poppe

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 07-2015

MSC 2000

34A09 Implicit equations, differential-algebraic equations
93B40 Computational methods

Abstract :
We consider the (sub)optimal $\mathcal{H}_{\infty}$-control problem for discrete time descriptor systems. Necessary and sufficient optimality conditions are derived in terms of deflating subspaces of palindromic matrix pencils. This approach allows the use of structure preserving matrix techniques which lead to a more robust method compared with currently used algorithms. The approach is suitable for standard systems as well as for index one and higher index systems. We illustrate the results by a numerical example.

Keywords : Discrete-time system, robust control, palindromic pencil, differential-algebraic equation,