Stability Analysis for Routh-Hurwitz Conditions Using Partial Pivot

Abstract Stability analysis of the polynomial characteristic equation is not easy to applied to a high-order system, in this case, it relates to search the roots of the degree n polynomial equation. It is difficult to find the roots of the equation, so stability analysis will be carried out using the stability of Routh-Hurwitz. In this study, a polynomial characteristic equation is given with a degree n with a real coefficient, then applied to the Hurwitz Matrix and a Gauss elimination procedure with a partial pivot is performed, then the growth factor is calculated. The results showed that the polynomial characteristic equation of degree n for Routh-Hurwitz conditions is said to be stable if each zero of the polynomial is located in the half left open field if and only if the elimination procedure can be performed and the optimal value of growth factor is 1.