• A necessary condition for stability of the system is that all of the roots of its characteristic equation have negative real parts, which in turn requires that all the coefficients be positive.
• A necessary (but not sufficient) condition for stability is that all the coefficients of the polynomial characteristic equation are positive & none of the co-efficient vanishes.
• Routh’s formulation requires the computation of a triangular array that is a function of the coefficients of the polynomial characteristic equation.
• A system is stable if and only if all the elements of the first column of the Routh array are positive
Method for determining the Routh array
Consider the characteristic equation
a(s) = a0sn + a1sn-1 + a2sn-2 + ....+ an-1s1 + ans0
