Improving the Robustness of Multivariable Linear Quadratic Regulator via Parametric Design

Based on the recently developed parametric feedback design methods for linear time invariant systems (LTIS), this paper presents a sub-optimal state feedback controller for LTIS involving structured real-valued plant parameter uncertainties. Based upon an optimality for the parametric feedback to be LQR optimal, a new performance index function, Jr, for the measure of both robustness and dynamic performance, is constructed. By minimizing Jr, a sub-optimal state feedback controller with higher robustness than that of the LQR controller under the performance index function Jl. A simulation example of a fifth-order system with structure uncertainties is considered and desirable results are obtained.