Synthesis of optimal H-infinity controllers is formulated as a loop-shaping problem where the desired closed-loop shape to be pursued is a uniform frequency response of the largest singular value. The weighted H-2 optimization technique used in the linear quadratic Gaussian design with loop transfer recovery is exploited in the loop-shaping procedures to generate a sequence of H-2 controllers converging to the optimal H-infinity controller. The resulting optimal H-infinity controller not only has the inherent robust property due to H-infinity criterion but also possesses the nice H-2 control structure, being easy to compute and implement. A fighter example and a large space structure example are demonstrated to show that the numerical accuracy of the present H-2-based H-infinity synthesis is comparable to the conventional H-infinity approach, i.e., gamma-iteration, but with reduced computational efforts. References: 17
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