  The paper is concerned with asymptotic stability properties of linear
switched systems. Under the hypothesis that all the subsystems share a non
strict quadratic Lyapunov function, we provide a large class of switching
signals for which a large class of switched systems are asymptotically stable.
For this purpose we define what we call non chaotic inputs, which generalize
the different notions of inputs with dwell time. Next we turn our attention to
the behaviour for possibly chaotic inputs. To finish we give a sufficient
condition for a system composed of a pair of Hurwitz matrices to be
asymptotically stable for all inputs.
