Overlapping control systems with delayed communication channels: Stability analysis and controller design

In this paper, a decentralized overlapping static output feedback law is proposed to control a linear time-invariant (LTI) interconnected system. It is assumed that an overlapping information flow structure is given which determines which output measurements are available for any local control agent. Uncertain transmission delay is also considered in communication links among different subsystems. Each subsystem is assumed to be subject to input disturbances with finite energy. A necessary condition for the existence of a stabilizing overlapping controller is obtained which is easy to check. Furthermore, a linear matrix inequality (LMI) based design methodology is proposed to achieve internal stability and H_infin disturbance attenuation. Simulations are presented to demonstrate the efficacy of the developed results.