The Routh-Hurwitz stability criterion

The work of Routii (i905) and Hurwitz (i875) gives a method of indicating the presence and number of unstabie roots, but not their vaiue. Consider the characteristic equation 

If (a) above is satisfied, then the necessary and sufficient condition for stability is either 

Routh s method is easy to apply and is usually used in preference to the Hurwitz technique. Note that the array can also be expressed in the reverse order, commencing with row. v . 

Cheek the stability of the system whieh has the following eharaeteristie equation 

st 1 All eoeffieients are present and have the same sign. Proeeed to Test 2, i.e. Routh s array 

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An inherently stable process can be destabilised by the addition of a feedback control loop—particularly where integral action is included. This is illustrated in the following example using the characteristic equation and the Routh-Hurwitz stability criterion. 

Bilinear transformation to map the interior of the unit circle in the z-plane onto the left half of the complex variable -plane. (Application of the Routh-Hurwitz stability criterion). ... 

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