Stability of switching infinite-dimensional systems

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@?(t)=A"ix(t), i@?{1,2}, when the infinitesimal generators A"1 and A"2 commute. In addition, the existence of a common quadratic Lyapunov function is demonstrated.