Network realizability for interconnected systems over arbitrary one-step delay networks

In our previous work, we developed a network realizability theory for interconnected systems over causal communication networks. In this paper, we extend those ideas to develop a notion of network realizability for systems over one-step delay networks. The dynamics of individual subsystems of the interconnected system along with the delays on the network links are used to analyze state-space and input-output descriptions of interconnected systems designed over one-step delay networks. The constraints for network realizability are derived and later used in designing optimal distributed H₂ controllers over one-step delay networks for a class of interconnected plants.