Decentralized Stabilization of Discrete-Time Networked Strongly Coupled Complex Systems

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.

[1]  Manuel de la Sen,et al.  Non-Fragile Controllers for a Class of Time-Delay Nonlinear Systems , 2009, Kybernetika.

[2]  Peng Shi,et al.  Sampled-data control of networked linear control systems , 2007, Autom..

[3]  James Lam,et al.  Stabilization of linear systems over networks with bounded packet loss , 2007, Autom..

[4]  John Baillieul,et al.  Handbook of Networked and Embedded Control Systems , 2005, Handbook of Networked and Embedded Control Systems.

[5]  J.P. Hespanha,et al.  Optimal communication logics in networked control systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[6]  Yingwei Zhang,et al.  Stabilization of networked control systems , 2006, 2006 1st International Symposium on Systems and Control in Aerospace and Astronautics.

[7]  A. Matveev,et al.  Estimation and Control over Communication Networks , 2008 .

[8]  Long Wang,et al.  An LMI approach to networked control systems with data packet dropout and transmission delays , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  D. Siljak,et al.  Robust stability and stabilization of discrete-time non-linear systems: The LMI approach , 2001 .

[10]  Tamer Basar,et al.  Communication Constraints for Decentralized Stabilizability With Time-Invariant Policies , 2007, IEEE Transactions on Automatic Control.

[11]  T. Başar,et al.  Quantization and coding for decentralized LTI systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[12]  Robin J. Evans,et al.  Stabilising decentralised linear systems under data rate constraints , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[13]  Sigurd Skogestad,et al.  Control of symmetrically interconnected plants , 1994, Autom..

[14]  M. de la Sen,et al.  Decentralized stabilization of networked complex composite systems with nonlinear perturbations , 2009, 2009 IEEE International Conference on Control and Automation.

[15]  Panos J. Antsaklis,et al.  Networked Embedded Sensing and Control , 2006 .

[16]  Zhou Lei,et al.  Stabilization of discrete-time networked control systems with nonlinear perturbation , 2008, 2008 27th Chinese Control Conference.

[17]  J. Hespanha,et al.  Communication logics for networked control systems , 2004, Proceedings of the 2004 American Control Conference.

[18]  D. Ho,et al.  Robust stabilization for a class of discrete-time non-linear systems via output feedback: The unified LMI approach , 2003 .

[19]  Lubomír Bakule,et al.  Decentralized control: An overview , 2008, Annu. Rev. Control..

[20]  Junyu Wei.  Stability analysis of decentralized networked control systems , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[21]  T. Başar,et al.  On the absence of rate loss in decentralized sensor and controller structure for asymptotic stability , 2006, 2006 American Control Conference.