A Simple Derivation of Are Solutions to the Standard H∞control Problem Based on Lmi Solution

The ”two Riccati equation” solution (ARE solution hereafter) to the standard H∞control problem was first presented in 1988 in a paper by Glover and Doyle[3] (GloverDoyle solution hereafter) without proof. The complete proof is given in [5] based on the so-called four-block problem. The derivation of this solution requires quite high level mathematical techniques and is so complicated that, to the knowledge of the authors, no textbooks are able to include this proof. A more system-oriented approach was published in the famous paper by Doyle, Glover, Khargonekar and Francis[1] in 1989. This solution is widely known as the DGKF solution and inspired numerous related researches afterwards. This DGKF solution and Glover-Doyle solution paved the way towards the applications of H∞control. Although the approach of [1] is theorectically sophisticated and self-contained, it is still not easy for ordinary control engineers to understand.