The Routh Array is

                                                    Table IV.3: Routh Array of eq. (IV.45)

Only the third element of the first column is capable of being negative due to inappropriate choice of controller parameters. The stability of the closed loop system will be ensured if

For example at , then the condition of stability is ensured if

 

IV.3.4 Root Locus analysis

The root locus analysis is an useful tool for determining the stability characteristics through graphical means. Root loci are plotted in complex plane as the gain varies from zero to infinity.