The paper demonstrates that a common quadratic Lyapunov function exists for all linear systems of the form x = A(i)z, i = 1, 2,.., N, where the matrices A(i) are asymptotically stable and commute pairwise. This in turn assures the exponential stability of a switching system x(t) = A(t)x(t) where A(t) switches between the above constant matrices A(i).