Improved Procedure for Robustness Regions Design

The design problem of robustness controllers for LTI systems is a fundamental problem in control theory. Some robustness region methods for PID controllers based on frequency design specifications (e.g. conditions on the maximum of sensitivity and complementary sensitivity functions) were published recently. However, these methods find all roots of a high order polynomial equation in each step and consequently are very demanding with respect to computation time. The paper introduces more effective procedure for determination of robustness regions based on the classical Laguerre's root finding algorithm.