We consider linear systems of differential equations $I \ddot{x}+B
\dot{x}+C{x}={0}$ where $I$ is the identity matrix and $B$ and $C$
are general complex $n$ x $n$ matrices. Our main interest is to
determine conditions for complete marginalstability of these
systems. To this end we find solutions of the Lyapunov matrix
equation and characterize the set of matrices $(B, C)$ which
guarantees marginal stability. The theory is applied to gyroscopic
systems, to indefinite damped systems, and to circulatory systems,
showing how to choose certain parameter matrices to get sufficient
conditions for marginal stability.Comparison is made with some
known results for equations with real system matrices.Moreover
more general cases are investigated and several examples are given.

Number of pages | 11 |
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Publication status | Published - 2000 |
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