Quantitative Analysis of Controller Design Localizability

Abstract

In this paper, we propose an index of the localizability for the distributed design of local controllers. We consider the case where a large-scale system is controlled by a retrofit controller. The retrofit controller is a local plug-in controller such that, rather than an entire system model, only a model of the subsystem of interest is required for the controller design. The localizability index is defined as the H_∞ norm of an error system defined based on the isolation of the subsystem of interest from the entire system. The proposed index measures how much the control performance of the subsystem of interest is invariant with respect to the variation of subsystems other than the subsystem of interest. Then, we show that the localizability index is estimated from only the model parameters of the subsystem of interest. Finally, a retrofit controller placement problem for power systems is analyzed by the localizability index.