Sampled-Data Synchronization of Chaotic Lur’e Systems with Stochastic Sampling

In this paper, we study the problem of master–slave synchronization for chaotic Lur’e systems with sampled-data control. The sampling intervals are assumed to satisfy a Bernoulli distributed white noise sequence with fixed and given occurrence probability. By applying an input-delay approach, the probabilistic sampling system is transformed into a continuous time-delay system with stochastic parameters in the system matrices. Based on Lyapunov functional approach, a sufficient condition of exponentially mean-square synchronization is obtained by analyzing the corresponding synchronization error systems. The controller gains are designed by solving a set of linear matrix inequalities. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method.

[1]  Hamid Reza Karimi,et al.  Data-driven adaptive observer for fault diagnosis , 2012 .

[2]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[3]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

[4]  Zhanshan Wang,et al.  Anti-Synchronization of Markovian Jumping Stochastic Chaotic Neural Networks with Mixed Time Delays , 2014, Circuits Syst. Signal Process..

[5]  P. Mahadevan,et al.  An overview , 2007, Journal of Biosciences.

[6]  Dan Zhang,et al.  Energy-efficient H∞ filtering for networked systems with stochastic signal transmissions , 2014, Signal Process..

[7]  Dong Yue,et al.  Stabilization of Systems With Probabilistic Interval Input Delays and Its Applications to Networked Control Systems , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[8]  Chun Yin,et al.  Design PD controller for master–slave synchronization of chaotic Lur’e systems with sector and slope restricted nonlinearities ☆ , 2011 .

[9]  Dan Wei,et al.  Global exponential synchronization of nonlinear time-delay Lur'e systems via delayed impulsive control , 2014, Commun. Nonlinear Sci. Numer. Simul..

[10]  Qing-Long Han,et al.  On Designing Time-Varying Delay Feedback Controllers for Master–Slave Synchronization of Lur'e Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  Tae H. Lee,et al.  Stochastic sampled-data control for state estimation of time-varying delayed neural networks , 2013, Neural Networks.

[12]  Johan A. K. Suykens,et al.  Master-Slave Synchronization of Lur'e Systems with Time-Delay , 2001, Int. J. Bifurc. Chaos.

[13]  Hong-yong Yang,et al.  New globally asymptotical synchronization of chaotic Lur'e systems using sampled data , 2010, Proceedings of the 2010 American Control Conference.

[14]  Min Wu,et al.  Asymptotical synchronization for chaotic Lur'e systems using sampled-data control , 2013, Commun. Nonlinear Sci. Numer. Simul..

[15]  M. Buoncristiani,et al.  Stochastic sampling effects in STR typing: Implications for analysis and interpretation. , 2014, Forensic science international. Genetics.

[16]  Wu-Hua Chen,et al.  Impulsive synchronization of chaotic Lur'e systems via partial states , 2008 .

[17]  David J. Hill,et al.  Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[18]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[19]  Dong Yue,et al.  Delay-Distribution-Dependent Stability and Stabilization of T–S Fuzzy Systems With Probabilistic Interval Delay , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  P. Balasubramaniam,et al.  Secure Communication via Synchronization of Lur’e Systems Using Sampled-Data Controller , 2014, Circuits Syst. Signal Process..

[21]  Meiqin Liu,et al.  Delayed Standard Neural Network Models for Control Systems , 2007, IEEE Transactions on Neural Networks.

[22]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  A. Isidori.  Nonlinear Control Systems , 1985 .

[24]  T. Yokoyama,et al.  Variable Sampling Quasi Multirate Deadbeat Control Method for Single Phase PWM Inverter in Low Carrier Frequency , 2007, 2007 Power Conversion Conference - Nagoya.

[25]  Xiaoming Chen,et al.  H∞ filtering with stochastic sampling , 2010, Signal Process..

[26]  S. M. Lee,et al.  Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control , 2009 .

[27]  Huijun Gao,et al.  Data-Based Techniques Focused on Modern Industry: An Overview , 2015, IEEE Transactions on Industrial Electronics.

[28]  Ju H. Park,et al.  Synchronization Criterion for Lur’e Systems via Delayed PD Controller , 2010, J. Optim. Theory Appl..

[29]  Min Wu,et al.  Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  Zidong Wang,et al.  Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling , 2012, IEEE Transactions on Automatic Control.

[31]  David J. Hill,et al.  Impulsive Synchronization of Chaotic Lur'e Systems by Linear Static Measurement Feedback: An LMI Approach , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  Hamid Reza Karimi,et al.  Data-driven design of robust fault detection system for wind turbines , 2014 .

[33]  J. Suykens,et al.  Nonlinear H/sub /spl infin// synchronization of Lur'e systems: dynamic output feedback case , 1997 .

[34]  Hongye Su,et al.  Asymptotical Synchronization of Chaotic Lur’e Systems Under Time-Varying Sampling , 2013, Circuits, Systems, and Signal Processing.

[35]  P. Apkarian,et al.  A Linear Matrix Inequality Approach toH 1 , 1994 .

[36]  J. Suykens,et al.  Nonlinear H Synchronization of Lur ’ e Systems : Dynamic Output Feedback Case , 1997 .

[37]  Wu-Hua Chen,et al.  On Sampled-Data Control for Master-Slave Synchronization of Chaotic Lur'e Systems , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[39]  Huijun Gao,et al.  Distributed Robust Synchronization of Dynamical Networks With Stochastic Coupling , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[41]  Lei Zhou,et al.  Synchronization of chaotic Lur'e systems with quantized sampled-data controller , 2014, Commun. Nonlinear Sci. Numer. Simul..

[42]  Steven X. Ding,et al.  Data-driven monitoring for stochastic systems and its application on batch process , 2013, Int. J. Syst. Sci..

[43]  Rong Li,et al.  Adaptive Synchronization of Complex Dynamical Networks with Time-Varying Delays , 2013, Circuits, Systems, and Signal Processing.

[44]  Jinde Cao,et al.  Synchronization Error Estimation and Controller Design for Delayed Lur'e Systems With Parameter Mismatches , 2012, IEEE Transactions on Neural Networks and Learning Systems.