All fixed-order H∞ controllers: observer-based structure and covariance bounds

This note obtains a parameterization of the set of all stabilizing controllers of order less than or equal to the plant, which yields for the closed-loop transfer matrix a specified H_∞ norm bound. The algebraic results of covariance control are applied to the H _∞ control problem to yield a parameterization in terms of the Lyapunov matrix, which carries many system properties (such as H ₂ performance, covariance bounds, system entropy at infinity, etc.). All low-order H_∞ controllers are shown to have observer-based structure for “reduced-order models” of the plant and are characterized by two Riccati equations with a coupling condition