Performance bounds in ℋ_∞ optimal control for stable SISO plants with arbitrary relative degree

This note deals with performance bounds for the ℋ_∞ -optimal control of discrete-time LTI plants. The case studied corresponds to stable scalar plants with arbitrary relative degree but no finite non-minimum phase zero. By using Nehari's Theorem and a reformulation of the standard Youla Parameterization a closed-form expression for the characteristic polynomial of the associated eigenvalue problem is obtained. Also, we derive an analytic expression for the optimal ℋ_∞ cost as a function of the plant relative degree.