Approximate and Exact Controllability of Switched Infinite-Dimensional Linear Systems

This article addresses the approximate and exact controllability issues of switched infinite-dimensional linear systems. First, a controllability map that is related to switching sequence and a controllability Gramian operator are proposed, based on which two necessary and sufficient conditions are established for approximate and exact controllability, respectively. Second, it shows that the obtained conditions can degenerate into the existing controllability criteria of infinite-dimensional linear systems, switched finite-dimensional linear systems, and a single finite-dimensional linear system. Finally, the new results are applied to analyze the approximate controllability of switched linear parabolic systems and the exact controllability of switched linear wave systems. Two examples are given to illustrate the effectiveness of the proposed approaches.