Construction of low authority, nearly nonminimal LQG compensators for reduced-order control design

It has been observed numerically that suboptimal controller reduction methods tend to work well when applied to low authority LQG controllers. However, to date, a rigorous justification for this phenomena has not been established. This paper shows that for continuous-time stable systems, by proper choice of the structure of the design weights, the corresponding LQG compensator becomes nonminimal as the control authority is decreased. An example illustrates that the near nonminimality of the LQG compensator can result in near optimality of the corresponding controller obtained by suboptimal controller reduction.