This paper characterizes easily controllable single-input-single-output (marginally) stable continuous-time plants in a quantitative manner by way of best achievable performance in
H∞ loop shaping design. The characterization is based on a finite frequency phase/gain property, which we call Condition (π), and the achievable performance level for any 2nd order system satisfying this condition is proven to be bounded from above by the value γDI=√4+2√2. A simple procedure for the choice of a weighting function in
H∞ loop shaping design is proposed based on the obtained knowledge, and its effectiveness is confirmed by a numerical example.
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