Robust LQ Controller for Discrete-Time System with Matching Structured and Bounded Uncertainties

This paper presents a systematic way for selecting the weighting matrices Q, M and R of the cost function such that the optimal control law for the nominal system can stabilize the uncertain system. The method is based on the Lyapunov stability criterion and the so-called matching conditions of uncertainties (i.e. uncertainty which lies in the range of the system input matrix).