For the second order systems * Necessary condition of the Routh Hurwitz criteria implies sufficient condition Stability can not be determined using Routh Hurwitz criteria Asymptotic stability is always guaranteed BIBO stability implies asymptotic stability Asymptotic stability is guaranteed for the third order system if it has the characteristic polynomial where the * product of the coefficient of s*3 and the constant coefficient is smaller than the product of the coefficient of s^2 and the coefficient of s product of the coefficient of s*3 and the constant coefficient is larger than the product of the coefficient of s^2 and the coefficient of s product of the coefficient of s*3 and the constant coefficient is equal to the product of the coefficient of s^2 and the coefficient of s product of the coefficient of s^2 and the constant coefficient is smaller than the product of the coefficient of s*3 and the coefficient of s When there is a zero in the first column of the determinants in the Routh Tables. we proceed by * replacing the zero with an infinitesimally small number with any sign replacing the zero with an infinitesimally small number with positive sign replacing the zero with an infinitesimally small number with negative sign replacing the zero with a very large number with positive sign