Decentralized Stabilization of Discrete-Time Networked Strongly Coupled Complex Systems

In this paper, the authors present an approach to decentralized stabilization with delayed feedback for a class of networked discrete-time complex systems. A class of dynamic discrete-time systems with identical linear nominal subsystems, symmetric nominal interconnections, and nonlinear perturbations is considered. The proposed method is based on particular structural properties of these systems which enable to construct a reduced order control design model with equivalent dynamic properties as the original system. Then, the standard method of linear matrix inequalities is used to design the gain matrix for such reduced model. The effect of data-packet dropout and communication delays between the plant and the controller is included in the controller design. It is shown how this methodology can simplify the control design with time-varying delay in the input. For such a purpose, a delay-dependent approach is applied in order to obtain a robustly delay-dependent stable overall closed-loop system with a decentralized controller.