  This paper mainly deals with switched linear systems defined by a pair of
Hurwitz matrices that share a common but not strict quadratic Lyapunov
function. Its aim is to give sufficient conditions for such a system to be
GUAS.We show that this property of being GUAS is equivalent to the uniform
observability on $[0,+\infty)$ of a bilinear system defined on a subspace whose
dimension is in most cases much smaller than the dimension of the switched
system.Some sufficient conditions of uniform asymptotic stability are then
deduced from the equivalence theorem, and illustrated by examples.The results
are partially extended to nonlinear analytic systems.
