2.2.5 The Controller Design Using Constrained Feedback Stabilization
Selected for further experiments is a controller in the middle of the list lqcontrollers that adequately improves the damping factor and yet avoids extremely large feedback gains. In effect, this choice provides a reasonable compromise between the settling time of the system and the sensitivity of the feedback to the noise.
This selects the controller in the middle of the list.
This is a norm of the feedback gains.
This provides a measure of the noise sensitivity of the feedback.
These are the closed-loop poles for the selected feedback matrix.
This is a measure of the damping factor of the closed-loop system.
This uses the partial Lyapunov feedback stabilization to construct a state feedback controller that provides a comparable damping factor.
The norm of the feedback gain matrix is somewhat smaller than the one provided by the LQR design.
The noise sensitivity of the feedback is also smaller.
Here are the closed-loop poles. Note that the partial Lyapunov stabilization shifted the only noncompliant pole (the one at the origin) into the chosen region.