  In this preliminary work, we propose to use a polynomial approach in order to
study the stability of switched systems. The proposed strategy is based on the
Bernstein interpolation method that may transform a switched system into a
polynomial expression from which an associated "simple" Lyapunov function can
be eventually built. The HOL Light proof assistant allows verifying formally
the Lyapunov functions that are identified from the proposed switching
structure. Our approach is illustrated by numerical examples.
