On the Closed-Loop Structure of H^∞ Control Systems

Abstract

In this paper, we show that the order of the closed-loop H^∞ control systems using central controllers is determined by the sum of the numbers of stable 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. Furthermore, using this result, we derive a new explicit form of the closed-loop transfer function of H^∞ control systems based on the chain-scattering approach, which clarifies the fundamental structure of H^∞ control systems.