Through its rapid progress in the last decade, HOOcontrol became an established control technology to achieve desirable performances of con­ trol systems. Several highly developed software packages are now avail­ able to easily compute an HOOcontroller for anybody who wishes to use HOOcontrol. It is questionable, however, that theoretical implications of HOOcontrol are well understood by the majority of its users. It is true that HOOcontrol theory is harder to learn due to its intrinsic mathemat­ ical nature, and it may not be necessary for those who simply want to apply it to understand the whole body of the theory. In general, how­ ever, the more we understand the theory, the better we can use it. It is at least helpful for selecting the design options in reasonable ways to know the theoretical core of HOOcontrol. The question arises: What is the theoretical core of HOO control? I wonder whether the majority of control theorists can answer this ques­ tion with confidence. Some theorists may say that the interpolation theory is the true essence of HOOcontrol, whereas others may assert that unitary dilation is the fundamental underlying idea of HOOcontrol. The J­ spectral factorization is also well known as a framework of HOOcontrol. A substantial number of researchers may take differential game as the most salient feature of HOOcontrol, and others may assert that the Bounded Real Lemma is the most fundamental building block.