On preserving the robustness of an optimal control system with observers

A new, simple, and general method is proposed in this note to preserve the robustness of the LQ control system which involves state estimators. The method is to minimize the estimator gain to the system input by selecting the estimator poles, while the existing method is to maximize the estimator gain to the system output by introducing additional noise in the system input noise description. An example demonstrates that the stability margin of the feedback system with the estimator designed by this method is even better than that of a system without the estimators.