Design of an H∞ optimal controller by using DGKF´s state-space formulas

The two-Riccati-equation method was employed to design an H ^∞ optimal controller for a four-block problem. An iterative scheme was used to reduce γ to a number which is very close to the optimum. However, as γ approaches the optimum, the elements of the state-space realization of the controller approach infinity. It is demonstrated that the numerical difficulty is caused by the restriction of the controller´s being strictly proper. This difficulty can easily be removed by the use of a proper controller with a direct feed-through term