An Algebraic Formula for Performance Bounds of a Weighted $\mathcal {H}_\infty$ Optimal Control Problem

This article provides performance bounds for a particular H_∞ model-matching problem. We consider scalar linear time-invariant plants in a one-degree-of-freedom control loop. We obtained explicit expressions for the Gramians needed when Nehari's theorem is applied to this problem, leading to a simple algebraic equation for the optimal performance. This formula sheds light upon the effect that nonminimum-phase zeros have on the optimal performance and yields easily computable bounds and approximations.