A generalized Routh-Hurwitz criterion for the stability analysis of
polynomials with complex coefficients: application to the PI-control of
vibrating structures
The classical Routh-Hurwitz criterion is one of the most popular methods to
study the stability of polynomials with real coefficients, given its simplicity
and ductility. However, when moving to polynomials with complex coefficients, a
generalization exists but it is rather cumbersome and not as easy to apply. In
this paper, we make such generalization clear and understandable for a wider
public and develop an algorithm to apply it. After having explained the method,
we demonstrate its use to determine the external stability of a system
consisting of the interconnection between a rotating shaft and a PI-regulator.
The extended Routh-Hurwitz criterion gives then necessary and sufficient
conditions on the gains of the PI-regulator to achieve stabilization of the
system together with regulation of the output. This illustrative example makes
our formulation of the extended Routh-Hurwitz criterion ready to be used in
several other applications