Abstract
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 function p(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 for p. 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.
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