On the Perfect Output Regulation of High-Order Fully Actuated Systems with Zero Dynamics

The input-output normal form for high-order fully actuated systems (HOFASs) with the linear output and the welldefined relative degree is derived globally, based on the input-output normal form of linear systems. Then the problem of perfect output regulation for high-order fully actuated systems (HOFASs) is investigated using its normal form and the parametric Lyapunov equation approach. For the HOFAS with a linear output and a well-defined relative degree, the problem of perfect output regulation is solvable if and only if it is marginally minimum-phase, namely, its zero dynamics is marginally stable. This equivalence highlights the inherent performance limitation of strictly nonminimum-phase HOFASs.