Existence and global exponential stability of periodic solutions for coupled control systems on networks with feedback and time delays

In this paper, the existence and global exponential stability of periodic solutions for coupled control systems on networks with feedback and time delays (CCSFD) are considered. Several sufficient criteria are given to guarantee the existence and global exponential stability of periodic solutions for CCSFD by combining with coincidence degree theory, Lyapunov method, and graph theory. Furthermore, an application to a class of Lurie coupled control systems on networks is presented to show the feasibility of our results. In the end, a numerical test is presented to illustrate the effectiveness of our theoretical results.