H∞-control of discrete-time descriptor systems

We consider the (sub)optimal H∞-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