The Routh–Hurwitz stability criterion is a mathematical test used in control theory to determine the stability of a linear time-invariant (LTI) system based on the coefficients of its characteristic polynomial. Specifically, it helps assess whether all poles of the system's transfer function have negative real parts, which is a necessary condition for the system to be stable.
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The Routh-Hurwitz criterion tests whether all roots of a real polynomial have negative real part, by sign conditions on determinants formed from its coefficients. Applied to a characteristic polynomial, it gives an algebraic test for strict linear asymptotic stability.