Abstract
This letter proposes a new approach to design Proportional-Integral (PI) and Proportional-Integral-Derivative (PID) controllers. The main result is a constructive determination of the set $\mathcal {S}$ ( $\sigma $ ) of stabilizing PI and PID controllers with closed loop poles having real parts less than $-\sigma $ . The signature method is applied to obtain the set $\mathcal {S}$ ( $\sigma $ ) in the controller parameter space. Illustrative examples are included to describe the procedure of the proposed method and to find the maximum achievable $\sigma $ for a given plant.
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