A relaxed small-gain theorem for discrete-time infinite networks. (August 2022) - Noroozi, Navid; Mironchenko, Andrii; Wirth, Fabian R.
Abstract: We study input-to-state stability (ISS) of discrete-time networks of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for ISS with respect to a closed set and show the necessity of the proposed small-gain condition in case of exponentially ISS infinite networks. Moreover, we study the well-posedness of the interconnection based on the behavior of the individual subsystems. Finally, over-approximations of large-but-finite networks by infinite networks are studied and it is shown that all the stability and performance indices obtained for the infinite system can be transferred to the original finite one if each subsystem of the infinite network is individually ISS.