A Separation Principle for Output Feedback Discrete-Time H2 Guaranteed Cost Control

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.