Robust formulas for optimal controllers

We present formulas for the construction of optimal H ∞ controllers that can be implemented in a numerically robust way. We base the formulas on the γ -iteration developed in Benner, Byers, Mehrmann, and Xu (2007). The controller formulas proposed here avoid the solution of algebraic Riccati equations with their problematic matrix inverses and matrix products. They are also applicable in the neighborhood of the optimal γ , where the classical formulas may call for the inverse of singular or ill-conditioned matrices. The advantages of the new formulas are demonstrated by several numerical examples.