Classical LQ regulator applied to the system with nonzero excitations

The LQ regulators with state or output feedback, designed for nonzero plant initial conditions and zero external excitations and applied to the systems with nonzero excitations are considered. In the case of the LQ regulator with output feedback, zero external excitations and nonzero plant initial conditions it is shown that the regulator is optimal or suboptimal if its initial conditions are adequate or nonadequate to those of the plant, respectively. It is shown that the LQ regulators with state or output feedback applied to systems with nonzero excitations retain their optimality properties which however concern only the transients generated by the excitations. Additionally, a necessary condition of regulation for MIMO plant is formulated and proved.