Communication topology design for large-scale interconnected systems with time delay

Communication networks provide a larger flexibility with respect to the control design of large-scale interconnected systems by allowing the information exchange between the local controllers of the subsystems. The use of communication networks comes, however, at the price of non-ideal signal tranmission such as time delay which is a source of instability and deteriorates the control performance. This paper introduces an approach for the design of the communication topology for the distributed control of large-scale interconnected systems in order to optimize the whole system's performance in the presence of constant time delay. First, a decentralized control law that stabilizes the overall interconnected system is designed. Then the performance is improved by designing the distributed control law, i.e. allowing the controller of the subsystems to exchange information, by considering the time delay in the networks. As a novelty in this paper, the design of the communication topology between the controllers is also considered. The problem is formulated as a mixed-integer optimization problem. Furthermore, a method based on matrix perturbation theory is discussed to design the topology which also captures the relation between the time delay, controller gain and performance of the overall system. In addition, it is shown that the proposed strategy also guarantees the stability of the overall system under the permanent communication link failure. The results are validated through a numerical example.