A wider class of stable gyroscopic systems

It is well-known that, in a physically interesting sense, n×n gyroscopic systems of the form L(λ)=λ2I+λB+C, where C>0 and B is indefinite and invertible, are stable whenever B>kI+k−1C for some real k>0. It is shown that stability is retained under a considerably weaker condition formulated in terms of the spectral radius of B−1(ωI+ω−1C).