PID Controller Synthesis Using a $\sigma$ -Hurwitz Stability Criterion

This letter proposes a new approach to design Proportional-Integral (PI) and Proportional-IntegralDerivative (PID) controllers. The main result is a constructive determination of the set 8(σ) of stabilizing PI and PID controllers with closed loop poles having real parts less than -σ. The signature method is applied to obtain the set 8(σ) in the controller parameter space. Illustrative examples are included to describe the procedure of the proposed method and to find the maximum achievable σ for a given plant.