Linear quadratic Gaussian design for robust performance objectives

The authors describe a technique for selecting the weighting functions of the LQG/LTR (linear quadratic Gaussian/loop transfer function recovery) formal synthesis procedure to satisfy a robust performance objective. The objective of the feedback system design problem is to achieve a small structured singular value over all frequencies. Existing formal synthesis approaches are used to generate the compensator by selecting the design parameters of the formal synthesis techniques to achieve objectives specified in terms of the structured singular value. The authors consider a problem of tracking an exogenous reference signal (command-following) in the presence of an unstructured multiplicative modeling error at the plant input. For this problem, the characteristics of closed-loop systems which result in a small structured singular value have been identified and quantified. Two formal synthesis approaches for this problem are considered: H ₂-optimization and H_∞-optimization