A simple derivation of ARE solutions to the standard H∞H∞ control problem based on LMI solution

In this note, a simple derivation of the Riccati equation based solutions to the standard H∞H∞ control problem, namely the well-known Glover–Doyle solution and DGKF solution is given based on LMI solution. It is hoped that this will be helpful in deepening the understanding of Riccati equation solutions.