As a distinct characterization of practical systems, the HOFAS is defined by the invertibility of its control matrix. Consequently, a methodology termed the HOFAS approach was proposed to efficiently resolve various control challenges [6]. This approach offers two key merits: (1) it streamlines controller design and overcomes limitations in model reduction, particularly when coupling terms exist within such systems; (2) it ensures full-actuation properties. Along this research trajectory, a series of relevant investigations have been conducted.