A Characterization of All Retrofit Controllers

In this paper, we give a characterization of all retrofit controllers for control of large-scale network systems. A retrofit controller is a local plug-in controller such that, rather than an entire network system model, only a model of the subsystem of interest is required for controller design. The retrofit controller guarantees the entire system stability for any (norm-unbounded) variations of neighboring subsystems, other than the subsystem of interest, as long as the network of the subsystem and neighboring subsystems is stable. Although a design procedure of a retrofit controller has been already proposed, how to characterize all retrofit controllers still remains an open question. We consider two cases where the interconnection signal is available and unavailable as a feedback signal. It is revealed that, in the case where the interconnection signal is available, all retrofit controllers are composed of a localizing compensator that cancels out the input-to-output map from the interconnection signal to the measurement signal, and a local controller that locally stabilizes the subsystem. It is also found that, in the case where the interconnection signal is unavailable, the effect from the measurement signal to the control input must be cancelled out in the controller. Finally, the effectiveness of retrofit control is verified through a numerical example of a benchmark model representing the bulk power system in the eastern half of Japan.