On the structure of H∞ controllers

Recently developed two-Riccati solutions to the H_∞-optimal control problem are considered. Two equivalent controller struct are shown to result from solution of two dual control problems. Separation arguments reminiscent of the typical LQG controlle form are used to demonstrate that the underlying estimation problem of H_∞ control is plant state reconstruction. Unlike the H₂ case, these H_∞-optimal controllers additionally require estimation of either the plant exogenous input or its controlled output based on the current plant state estimate. The subsequent discussion establishes a parallel between the H₂ and H_∞ approaches.