Characteristic equation
Characteristic equation the polynomial equation that results when the characteristic function is equated to zero. Its roots gives the singularities of the transfer function model, which in turn determine its transient behavior. Specifically, any root of the characteristic equation that has a negative real part indicates a stable decaying transient, while any root with a positive real part indicates an unstable growing transient. Any root with zero real part indicates a marginally stable transient that neither decays nor grows. The imaginary part of the root gives the frequency of oscillation of the transient signal. See also characteristic function.
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Author of the text: Ed. P.A. Laplante Boca Raton: CRC Press LLC, 2000
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