LQG balancing and reduced LQG compensation of symmetric passive systems†

Abstract
In this paper, a technique for balancing a system in a closed-loop fashion is developed. This technique is referred to as ‘LQG balancing’, for it assumes that the system to be balanced is closed up with a standard LQG feedback loop. This paper focuses on LQG balancing of symmetric passive systems; such systems are used to model large vibrating structures with collocated rate sensors and actuators. A balancing characterization of reciprocity, passivity and losslessness is provided. A new method for reducing both the plant and the LQG compensator is developed. It is shown, using a hyperstability argument, that the loop made up with the full plant and any reduced LQG compensator is stable and has acceptable feedback properties.

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