PID controller design with an H∞ criterion

This paper deals with the design of Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers. The main result is a constructive determination of the set S γ of stabilizing PI and PID controllers achieving an H∞ norm bound of γ on the error transfer function. This result utilizes the computation of the complete stabilizing set S recently obtained. We also point out connections between this H∞ design and Gain and Phase Margin designs. Illustrative examples are presented.