The Routh-Hurwitz Criterion is a mathematical test used to determine the stability of a linear time-invariant system by analyzing the characteristic polynomial's coefficients. It provides a systematic way to ascertain whether all poles of the system's transfer function lie in the left half of the complex plane, which is essential for ensuring system stability. This criterion is closely related to eigenvalue analysis, as the location of these poles corresponds to the eigenvalues of the system's state matrix, and it also ties into participation factors that help in understanding how changes in system parameters affect stability.
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