Migration of Roots When using the 'Epsilon Method' of the Routh-Hurwitz Criterion

P.C. Byrne (USA)


Routh-Hurwitz, stability test, `epsilon method'.


: When a characteristic polynomial has simple or multiple roots on the imaginary axis application of the `epsilon method' of the Routh-Hurwitz (R-H) criterion results in migration of these roots. In the examples considered, all drawn from the literature, it is shown that the `epsilon method' changed one of the coefficients of the characteristic polynomials. The modified polynomials are derived and the resulting polynomials' roots are obtained for arbitrary small positive and negative values of epsilon. It is shown, in each case considered, that the R-H Criterion, applied to the modified polynomials, correctly predicted the right hand plane (RHP) roots.

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