Decentralized Stabilization of Discrete-Time Networked Strongly Coupled Complex Systems Lubom´ ır Bakule ∗ , Dana Bakulov´ a ∗∗ , Martin Pap´ ık ∗ ∗ Institute of Information Theory and Automation Academy of Sciences of the Czech Republic 182 08 Prague 8, Czech Republic (bakule@utia.cas.cz) ∗∗ Center for Administration and Operations Academy of Sciences of the Czech Republic 110 00 Prague 1, Czech Republic Abstract: 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. Keywords: Decentralization, large-scale systems, complex systems, discrete-time systems, networked control systems INTRODUCTION A control system is called a networked control system (NCS) if its feedback loops are closed-via a shared com- munication medium. The medium limited capacity in a networked control system must be allocated to all feed- back loop components, i.e. the sensors, controller, and actuators. Therefore, various communication constraints such as delays, dropouts, data rate limitations, or quanti- zation effects are potential source of problems influencing on closed-loop system stability and performance. There are two general NCS configurations: Direct structure and Hierarchical structure. The NCS in the direct structure is composed of a controller and a remote system containing a physical plant, sensors, and actuators. The controller and the plant are physically located at different places. They are linked by a data network in order to operate in a remote closed-loop. The basic hierarchical structure consists of a main controller and a remote closed-loop sys- tem. The main controller computes and sends the reference signal via a network to the remote controller. The remote system then processes this signal to perform local closed- loop control and sends sensor measurement to the main controller for networked closed-loop control. This paper is 1 The authors are grateful to the Academy of Sciences of the Czech Republic by its support through the Grant IAA200750802. focused on the direct structure and deals with the inclusion of delays and dropouts in the feedback loop. Prior Work Recent surveys on the emerging area of networked control systems (NCS) can be found in Hristu-Varsakelis and Levine [2005], Antsaklis and Tabuada [2006], Matveev and Savkin [2009], but there is no unified and complete theory in this subject. Reference Xiong and Lam [2007] is focused on stabilization of NCS from the point of view of zero-order hold. The reference Hu et al. [2007] deals with time-driven digital controller and event-driven holder for NCS. It includes the possibility to deal with time delays and packet dropouts. Stabilization of discrete-time networked control systems is presented in Zhou et al. [2008] and Yu et al. [2004], while the references Stipanovi´ c and ˇ Siljak [2001] and Ho and Lu [2003] deal with stabilization by using the LMI approach. Decentralization generally means that the overall system task can be decomposed into several subsystem tasks so that the solution of subsystem tasks satisfactorily solves the overall system task. Decentralized NCS (DNCS) are the control systems with multiple control stations while transmitting control signals through a network, i.e. date signals are transmitted to multiple controllers in