Let p(s) be a polynomial, all of whose roots lie in the left half plane. The purpose of this note is to show that when the transfer functionp(0)/p(s)tracks unit step input, the integral square error (ISE) of the response has a simple expression in terms of the Routh—Hurwitz determinants forp. This enables us to generalize a result of Hall : he pointed out that for a quadratic polynomial with fixed natural frequency, the minimum ISE is attained for a damping factor of ½. We find the corresponding result for polynomials of any degree.