Non‐fragile robust control for networked control systems with long time‐varying delay, randomly occurring nonlinearity, and randomly occurring controller gain fluctuation

SUMMARY This paper investigates the non-fragile robust control problem for a class of nonlinear networked control systems (NCSs) with long time-varying delay. Both the uncertain nonlinearity and the controller gain fluctuation enter into the system in random ways, and such randomly occurring nonlinearity and randomly occurring controller gain fluctuation obey certain mutually uncorrelated Bernoulli distributed white noise sequences. A new time-varying discrete time system model is proposed to describe the NCS. To reduce conservatism arising from modeling time-varying parts, the time-varying parts due to the time-varying delay are treated as a norm-bounded uncertainty with one nominal point using robust control techniques. Based on the obtained uncertain system model, a regular and an optimal sufficient non-fragile controllers are derived by applying the Lyapunov stability theory and the linear matrix inequality technique, which render the closed-loop NCS to be asymptotically stable and guarantee an upper bound of the given performance cost for all admissible uncertainties. Moreover, the existence condition and design method for the non-fragile stabilizing controllers are also presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.

[1]  Linda Bushnell,et al.  Stability analysis of networked control systems , 2002, IEEE Trans. Control. Syst. Technol..

[2]  C. Loan.  The Sensitivity of the Matrix Exponential , 1977 .

[3]  Peng Shi,et al.  Sampled-Data Synchronization of Chaotic Lur'e Systems With Time Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Jun Yang,et al.  T-S Fuzzy-Model-Based Robust $H_{\infty}$ Design for Networked Control Systems With Uncertainties , 2007, IEEE Transactions on Industrial Informatics.

[5]  Xiao-Zheng Jin,et al.  Active coupling and its circuitry designs of chaotic systems against deteriorated and delayed networks , 2012 .

[6]  Xiaodong Liu,et al.  Stability analysis for neural networks with time-varying delay , 2008, 2008 47th IEEE Conference on Decision and Control.

[7]  Ju H. Park,et al.  Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control , 2013, Int. J. Control.

[8]  A. Jadbabaie,et al.  Robust non-fragile LQ controllers: the static state feedback case , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[9]  Young Soo Suh.  Stability and stabilization of nonuniform sampling systems , 2008, Autom..

[10]  Wen-An Zhang,et al.  A Robust Control Approach to Stabilization of Networked Control Systems with Short Time-varying Delays , 2010 .

[11]  Jianliang Wang,et al.  Non-fragile Hinfinity control for linear systems with multiplicative controller gain variations , 2001, Autom..

[12]  Ju H. Park,et al.  Robust sampled-data control with random missing data scenario , 2014, Int. J. Control.

[13]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[14]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .

[15]  Yong Zhang,et al.  Non-fragile control for nonlinear networked control systems with long time-delay , 2009, Comput. Math. Appl..

[16]  Ya-Jun Pan,et al.  Stabilization of remote control systems with unknown time varying delays by LMI techniques , 2006 .

[17]  Joseph R. Corrado,et al.  Robust resilient dynamic controllers for systems with parametric uncertainty and controller gain variations , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

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

[19]  Huaguang Zhang,et al.  Novel compensation-based non-fragile H ∞ control for uncertain neutral systems with time-varying delays , 2012, Int. J. Syst. Sci..

[20]  Ju H. Park,et al.  Non-fragile synchronization of neural networks with time-varying delay and randomly occurring controller gain fluctuation , 2013, Appl. Math. Comput..

[21]  Jun Hu,et al.  Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities , 2012, IEEE Transactions on Industrial Electronics.

[22]  Wen-An Zhang,et al.  BIBO stability and stabilization of networked control systems with short time‐varying delays , 2011 .

[23]  Wei Zhang,et al.  Stability of networked control systems , 2001 .

[24]  Jun Yang,et al.  Fuzzy Model-Based Robust Networked Control for a Class of Nonlinear Systems , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.