Real Km-Synthesis via Generalized Popov Multipliers

In this paper, we refine our H
^∞
control designs presented at the 1990 and 1991 American Control Conference by introducing a new "real K
_m
-Synthesis" technique involving the use of generalized Popov multipliers. Our multiplier technique substantially reduces, and in some cases may even eliminate altogether, the conservativeness associated with traditional K
_m
-Synthesis solutions in which all uncertainties are treated as complex, even when they arise from real parameters such as the masses and spring constants in the benchmark problem. The design results demonstrate how this approach permits a very precise analysis of the intrinsic tradeoffs between robustness, performance and control energy requirements. Also included is an open-loop H
^∞
prefilter design that allows one to address the command response shaping issue.