The Largest Achievable Delay Margin of a Class of Coupled LTI Systems Synthesized by Graph Operations

We investigate the dynamics of a class of coupled LTI systems in which LTI subsystems share information with each other under delays. In particular, the relationship between graph structures, graph synthesis and the delay margin associated with the arising graphs are studied. For this, we present a technique using Cartesian products to calculate the largest achievable delay margin when tailoring the Laplacians of graphs of the coupled systems. The calculation becomes possible by utilizing our Responsible Eigenvalue (RE) concept. Examples are provided to demonstrate the results.