This paper considers the output feedback H 2 guaranteed cost control problem. In [1], it was observed that exploiting the solution of a discrete algebraic Riccati equation corresponding to an optimal full information control design allowed the output feedback control problem, for a fixed value of a design parameter, to be reduced to a so-called full control problem in which only filter gains of an estimator needed to be designed. However, this critical result was not proved. This paper proves this result.

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