Simultaneous Synthesis of Weights and Controllers in H-Infinity Loop-Shaping

In this paper, several steps of the standard H∞ loop-shaping design procedure are combined into one optimization problem that maximizes the robust stability margin over the loop-shaping weights subject to constraints which ensure that the loop-shape and the singular values/condition numbers of the weights lie in pre-specified regions. Thus, loop-shaping weights, which can be required to have either a diagonal or a non-diagonal structure, and a robustly stabilizing controller are simultaneously synthesized by one algorithm in a systematic way. This approach greatly simplifies the often long and tedious process of designing “good” loop-shaping weights directly and allows the designer to quickly get an idea of what is attainable.