Distributed Design of Locally Stabilizing Controllers for Large-Scale Networked Linear Systems

In this paper, we consider designing locally stabilizing controllers, each of which stabilizes each disconnected subsystem, in a distributed manner for large-scale networked linear systems. To this end, we design a low-dimensional hierarchical distributed compensator such that the L-2-performance of the closed-loop system improves as long as that of the locally stabilizing controllers improves. We solve a controller reduction problem where the approximation error of the low-dimensional compensator gets better as long as the performance of the locally stabilizing controllers improves, while preserving the hierarchical distributed structure of the original compensator. Finally, we demonstrate the efficiency of the proposed method through a numerical example of a power network.