A robust numerical method for the γ-iteration in H∞ control

We present a numerical method for the solution of the optimal H∞ control problem based on the γ-iteration and a novel extended matrix pencil formulation of the state-space solution to the (sub)optimal H∞ control problem. In particular, instead of algebraic Riccati equations or unstructured matrix pencils, our approach is solely based on solving even generalized eigenproblems. The enhanced numerical robustness of the method is derived from the fact that using the structure of the problem, spectral symmetries are preserved. Moreover, these methods are also applicable even if the pencil has eigenvalues on the imaginary axis. We compare the new method with conventional methods and present several examples.