Matrix tests for stability
Biswa Nath Datta's paper Stability and
inertia (Linear Algebra and its Applications, Volumes 302-303, 1
December 1999, Pages 563-600) mentions three approaches for real
matrices: eigenvalue computation, Routh-Hurwitz, and Lyapunov eqn.
The usual way of solving the Lyapunov eqn numerically uses
eigenvalue factorisation, but it can be solved without eigenvalues,
as in the paper B.N. Datta & K. Datta, The matrix equation XA = A^TX
and an associated algorithm for inertia and stability, Linear Algebra
Appl. 97, 1987, 103109. This might be a good starting point for an
interval arithmetic stability tester.
From: Robert Piche (firstname.lastname@tut.fi)
http://math.tut.fi/~piche/