Importance of coefficient diagram in polynomial method

Coefficient Diagram Method (CDM) is one of polynomial methods in control design. Its design effectiveness mainly stems from the usage of a diagram called "Coefficient Diagram". Coefficient diagram shows the coefficients of characteristic polynomial and those of numerator polynomials corresponding to sensitivity and complementary sensitivity function in logarithmic scale, where the abscissa is the order for the coefficients. From the shape, designer can visualize the stability, response, and robustness. The frequency response of the sensitivity and complementary sensitivity function can be intuitively visualized, too. Thus H-inf problem can be solved without ordinary H-inf algorithm.