A wider class of stable gyroscopic systems

Abstract

It is well-known that, in a physically interesting sense, n× n gyroscopic systems of the form L( λ)= λ 2 I+ λB+ C, where C>0 and B is indefinite and invertible, are stable whenever | B|> kI+ k −1 C 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 −1 C).