The Routh-Hurwitz Stability Criterion, Revisited: The Case of Multiple Poles on Imaginary Axis

This technical note presents a relation between the number of zero rows (rows with all zero elements) in the Routh array and the multiplicity of
j
ω-axis poles. The main result of the technical note is that the existence of more than one zero row in the Routh array amounts to instability of the system irrespective of any sign change in the first column.