μ Synthesis using linear quadratic gaussian controllers

A sufficient condition is derived for the existence of the optimal μ controllers by showing the equivalence between the optimal μ problem and the weighted H₂-optimization problem. The weighted H₂-optimization technique used in linear quadratic Gaussian design with loop transfer recovery is exploited to generate a sequence of H₂ controllers converging to the optimal μ controller. The resulting optimal μ controller not only has the inherent robust-performance property resulting from the μ criterion, but also possesses the nice H₂ control structure, being easy to compute and implement. A flight control example is demonstrated to show that the numerical accuracy of the H₂-based μ-synthesis approach is comparable to the conventional H∞-based μ-synthesis technique (D-K iteration) but with reduced computational efforts.