Damping characteristics of the K-polynomial

As a standard form for the characteristic polynomial, the K-polynomial has been defined in terms of two specific parameters: a characteristic ratio and generalized time constant [1]. It allows us to synthesize all pole transfer function with such a K-polynomial denominator so that the model satisfies the prescribed overshoot and settling time. This note presents the damping property of the K-polynomial with respect to the characteristic ratio. The analysis was performed for a case where its degree is less than or equal to 5.