Strongly stable gyroscopic systems
Peter Lancaster · Electronic Journal of Linear Algebra · 1999
Here, gyroscopic systems are time-invariant systems for which motions can be characterized by properties of a matrix pencil L(λ) = λ 2 I + λG -C, where G T = -G and C > 0. A strong stability condition is known which depends only on |G| (= (G T G) 1/2 ≥ 0) 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| ≥ |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 |.