State feedback H∞ optimal control

Abstract

This chapter presents full information state feedback H∞ optimal control. This control synthesis method uses state space methods to achieve stability, performance, and robustness and allows for the direct loop shaping in the frequency domain. This chapter begins with an introduction of various norms used in control system design and analysis, followed by methods of specifying stability and performance specifications in the frequency domain. This logically leads into loop shaping using frequency-dependent weights. The state feedback control law is then synthesized using an algebraic Riccati equation approach called γ-iteration. This method is applied to a UAV design example. This control synthesis method is an excellent approach that teaches design engineers important properties in both the time domain and frequency domain and more importantly how to achieve these properties in a closed-loop design.