A simple but rich test example for H∞-optimal control

A simple second order feed-forward disturbance attenuation problem is analyzed. The problem has one free parameter, the control weight ρ in the loss function. It is found that controller structure and uniqueness for H_∞-control, in the optimal case, changes when ρ is varied. Sensitivity to initial conditions is also drastically changed. The example is simple enough to allow a solution by formula manipulation, but is rich enough to give physically reasonable controllers and insight into the behavior of both state-space and polynomial H_∞-methods at optimality. Details can be found in [6].