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)=Aix(t), i∈{1,2}, when the infinitesimal generators A1 and A2 commute. In addition, the existence of a common quadratic Lyapunov function is demonstrated.