In this note, we generalize the results from Narendra and Balakrishnan (IEEE Trans. Automatic Control 39 (1994) 2469) to the infinite-dimensional system theoretic setting. The paper gives results on the stability of a switching system of the form (x)over dot(i) = A(i)x(i). i is an element of {1, 2}, when the infinitesimal generators A(1) and A(2) commute. In addition. the existence of a common quadratic Lyapunov function is demonstrated. (C) 2004 Elsevier Ltd. All rights reserved.