Closed-loop structure of H∞ control

An explicit form of the closed-loop transfer function of H^∞ control systems is derived which clarifies the fundamental structure of H^∞ control systems. Based on this form, we show that the order of the closed-loop H^∞ control systems using central controllers is bounded by the sum of the numbers of unstable invariant zeros of P₁₂(s) and P₂₁ (s). This fact gives a sharp contrast with the LQG case where the order of the closed-loop system is always identical to that of the plant