Existence of dominant solutions in linear output feedback

The standard LQ-regulator is known to be a dominant controller in the sense that the optimal cost is minimal for all initial statesx_{0} \in R^{n}. In general, static or dynamic output feedback controllers do not have this dominance property. In this note, it is shown that in the general multivariable case and for the original cost functional, a dynamic output feedback controller using an observer is dominant if, and only if, the observer is perfectly initialized.