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Derivation of the Routh array
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<p>The Routh array is a <a href="/facts/Routh%25E2%2580%2593Hurwitz_stability_criterion/YNYfQr3F">tabular method</a> permitting one to establish the <a href="/facts/Stable_polynomial/lxJv9NSL">stability</a> of a system using only the coefficients of the characteristic <a href="/facts/Polynomial/Lzak8VVx">polynomial</a>. Central to the field of <a href="/facts/Control_theory/aIuERpn6">control systems design</a>, the <a href="/facts/Routh%25E2%2580%2593Hurwitz_theorem/SGsE7USb">Routh–Hurwitz theorem</a> and Routh array emerge by using the <a href="/facts/Euclidean_algorithm/wApql29c">Euclidean algorithm</a> and <a href="/facts/Sturm%2527s_theorem/fn2MG3wu">Sturm's theorem</a> in evaluating <a href="/facts/Cauchy_index/s48jHJhw">Cauchy indices</a>. </p>