The Routh-Hurwitz criterion determines stability using which part of the transfer function?

• A. The coefficients of the characteristic equation
• B. Only the constant term
• C. The numerator coefficients
• D. The imaginary parts of the zeros

Answer: (A)

The Routh-Hurwitz criterion is a mathematical method used to determine the stability of a linear time-invariant system by analyzing the characteristic equation of the system. The characteristic equation is derived from the denominator of the transfer function, which represents the system's dynamics.

In this context, the coefficients of the characteristic equation play a crucial role because they provide insights into the location of the system's poles in the complex plane. Stability is determined by the position of these poles; specifically, if all poles are in the left half of the complex plane, the system is stable. The Routh-Hurwitz criterion uses these coefficients to construct the Routh array, allowing you to infer the number of poles in the right half-plane.

The other answer choices focus on components that do not determine stability in this context. For instance, the constant term alone does not provide a complete picture of the system dynamics, while the numerator coefficients and the imaginary parts of the zeros are not relevant to stability determined via the Routh-Hurwitz criterion. Thus, focusing on the coefficients of the characteristic equation is essential to accurately assess system stability.