Robust Linear Quadratic Designs with Respect to Parameter Uncertainty

We derive a linear quadratic regulator which is robust to parametric uncertainty, by using the overbounding method of Petersen and Hollot. The resulting controller is determined from the solution of a single modified Riccati equation. We show that when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. We are also considering a worst-case disturbance in the direction of the uncertainty. Finally, we prove that we have increased performance robustness with the robust LQR when compared to a mismatched LQR design where we design the controller on the nominal system, but apply it to the actual uncertain system.