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 states xO??Rn. In general, static or dynamic output feedback controllers don´t have this dominance property. In this paper, 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.