LQR approach to robust stabilization of state space systems with matched uncertainties

This note shows an elegant relationship between the quadratic optimal control and robust stabilization for linear time-invariant (LTI) systems, where the former control can robustly stabilize the latter system, provided that the matched uncertainty is bounded. Through reviewing the relevant literature, some common mistakes in regard to this relationship are found. The correct results are obtained and proved in both frequency and time domains. The results are applicable to both single- and multi-input cases. They are significant as the simple LQR design for the nominal system can be utilized to directly solve-with no further effort-the complex robust stabilization problem for a class of linear uncertain systems.