The existence of common Lyapunov functions for switched systems is studied. For a special positive switched
systems, a sufficient condition for the existence of common Lyapunov functions is given. While the system matrices are a
compact set of second order matrices, a method of determining the existence of common Lyapunov functions is obtained,
and an algorithm of common Lyapunov function is presented. Finally, some examples are given to verify the effectiveness of
the proposed method.

common Lyapunov functions;switched systems;stability