ELA, Volume 5, pp. 53-66, March 1999, abstract.
Strongly Stable Gyroscopic Systems
Peter Lancaster
Here, gyroscopic systems are time-invariant systems for which motions can
be characterized by properties of a matrix pencil
L(lambda) = lambda^2 I + lambda G-C,
where G^T=-G and C>0. A strong stability condition is known which depends
only on |G| (equal to the square root of (G^T G) which is nonnegative)
and C. If a system with coefficients G_0 and C satisfies this condition then
all systems with the same C and with a G satisfying |G| greater tahn or equal
to |G_0| are also strongly stable. In order to develop a sense of those
variations in G_0 which are admissible (preserve strong stability), the class
of real skew-symmetric matrices G for which this inequality holds is
investigated, and also those G for which |G|=|G_0|.