A robust control system design by a parameter space approach based on sign difinite condition

A parameter space approach for robust control system design is developed by reducing several design specifications to sign definite conditions. It is shown that the gain and phase margin constraints for the parametric perturbed plant hold if and only if the four Kharitonov systems satisfy the margins. On pole location, it is shown that D-stability of convex combinations (1-t)p(s)+tq(s) can be determined by the coefficients corresponding to p(s) and q(s) based on the sign definite condition. We show a method of PI-type robust control system design as a useful example.