Fast and numerically robust algorithm for computing the H ∞ optimum

The authors present a fast and numerically stable algorithm for the computation of the optimal gain γ_opt in H _∞ control problems. The state-space characterization of γ_opt is used and the general case where D₁₁≠0 is considered. Convexity results are established for a criterion which synthesizes the usual conditions X ⩾0, Y⩾0, and ρ(XY)⩽γ² . This allows implementation of a Newton-like search method which achieves quadratic convergence to γ_opt. Special emphasis is placed on numerical stability. Finally, a thorough description of the algorithm is provided and its performance is compared with that of existing methods