scholarly journals MASTER–SLAVE SYNCHRONIZATION OF LUR'E SYSTEMS WITH TIME-DELAY

2001 ◽  
Vol 11 (06) ◽  
pp. 1707-1722 ◽  
Author(s):  
M. E. YALÇIN ◽  
J. A. K. SUYKENS ◽  
J. VANDEWALLE
Keyword(s):  
Time Delay ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Matrix Inequality ◽  
Lur’E Systems ◽  
Delay Effects ◽  
Feedback Matrix ◽  
Error System ◽  
Delay Dependent ◽  
Synchronization Scheme

In this paper time-delay effects on the master–slave synchronization scheme are investigated. Sufficient conditions for master–slave synchronization of Lur'e systems are presented for a known time-delay in the master and slave systems. A delay-dependent synchronization criterion is given based upon a new Lyapunov–Krasovskii function. The derived criterion is a sufficient condition for global asymptotic stability of the error system, expressed by means of a matrix inequality. The feedback matrix follows from solving a nonlinear optimization problem. The method is illustrated for the synchronization of Chua's circuits, 5-scroll attractors and hyperchaotic attractors.

SYNCHRONIZATION CRITERIA FOR LUR'E SYSTEMS BY DYNAMIC OUTPUT FEEDBACK WITH TIME-DELAY

2006 ◽  
Vol 16 (08) ◽  
pp. 2293-2307 ◽  
Author(s):  
XIA HUANG ◽  
JINDE CAO ◽  
DANIEL W. C. HO
Keyword(s):  
Time Delay ◽  
Output Feedback ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Dynamic Output Feedback ◽  
Lur’E Systems ◽  
Dynamic Output ◽  
Delay Dependent ◽  
Synchronization Scheme

In this paper a master-slave synchronization scheme is investigated by exploiting a dynamic output feedback control mechanism with time-delay and the influences of time-delay on synchronization are studied. Several new sufficient conditions, which are delay-independent or delay-dependent ones, are presented based on a general class of Lyapunov functions. The obtained results, expressed as matrix inequalities improve and generalize the earlier work in the literature and are readily verified via LMI control toolbox without tuning of parameters and/or matrices. The designs of the controller are implemented by solving a constrained nonlinear optimization problem. Finally, we illustrate our results on Chua's circuits and hyperchaotic attractors.

DELAY-DEPENDENT SYNCHRONIZATION CRITERION FOR LUR'E SYSTEMS WITH DELAY FEEDBACK CONTROL

2006 ◽  
Vol 16 (10) ◽  
pp. 3087-3091 ◽  
Author(s):  
YONG HE ◽  
GUILIN WEN ◽  
QING-GUO WANG
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Matrix Approach ◽  
Time Delay Systems ◽  
Stability Studies ◽  
Lur’E Systems ◽  
Weighting Matrix ◽  
Delay Feedback Control ◽  
Delay Dependent ◽  
Synchronization Scheme

A master-slave synchronization scheme for Lur'e systems is studied for a known delay existing between master and slave systems. Based on the latest development of stability studies for time-delay systems, a new delay-dependent synchronization criterion is derived by the free-weighting matrix approach. The criterion shown by example is less conservative than the existing synchronization criteria.

scholarly journals The Asymptotic Synchronization Analysis for Two Kinds of Complex Dynamical Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ze Tang ◽  
Jianwen Feng
Keyword(s):  
Time Delay ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Complex Dynamical Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Dynamical Networks ◽  
Simulation Results ◽  
Delay Dependent ◽  
Asymptotic Synchronization

We consider a class of complex networks with both delayed and nondelayed coupling. In particular, we consider the situation for both time delay-independent and time delay-dependent complex dynamical networks and obtain sufficient conditions for their asymptotic synchronization by using the Lyapunov-Krasovskii stability theorem and the linear matrix inequality (LMI). We also present some simulation results to support the validity of the theories.

Synchronization of chaotic Lur’e systems with state and transmission line time delay: a linear matrix inequality approach

2016 ◽  
Vol 39 (11) ◽  
pp. 1703-1709 ◽  
Author(s):  
Ali Kazemy ◽  
Mohammad Farrokhi
Keyword(s):  
Time Delay ◽  
Transmission Line ◽  
Linear Matrix ◽  
Multiple Time ◽  
Lur’E Systems ◽  
Chaotic Lur’E Systems ◽  
Delay Feedback Control ◽  
Error System ◽  
Linear Matrix Inequality Approach ◽  
Delay Dependent

This paper is concerned with the problem of the master–slave synchronization of chaotic Lur’e systems with multiple time delays in their states and transmission line. Based on the Lyapunov–Krasovskii functional, some delay-dependent synchronization criteria are obtained and formulated in the form of linear matrix inequalities (LMIs) to ascertain the global asymptotic stability of the error system such that the slave system is synchronized with the master. With the help of the LMI solvers, the time-delay feedback control law can easily be obtained. The effectiveness of the proposed method is illustrated using some numerical simulations performed on two chaotic systems.

scholarly journals Delay-Dependent Robust Stabilization for Nonlinear Large Systems via Decentralized Fuzzy Control

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chun-xia Dou ◽  
Zhi-sheng Duan ◽  
Xing-bei Jia ◽  
Xiao-gang Li ◽  
Jin-zhao Yang ◽  
...  
Keyword(s):  
Time Delay ◽  
Fuzzy Control ◽  
Upper Bound ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Large System ◽  
Disturbance Attenuation ◽  
Robust Controller ◽  
Large Systems ◽  
Delay Dependent

A delay-dependent robust fuzzy control approach is developed for a class of nonlinear uncertain interconnected time delay large systems in this paper. First, an equivalent T–S fuzzy model is extended in order to accurately represent nonlinear dynamics of the large system. Then, a decentralized state feedback robust controller is proposed to guarantee system stabilization with a prescribedH∞disturbance attenuation level. Furthermore, taking into account the time delays in large system, based on a less conservative delay-dependent Lyapunov function approach combining with linear matrix inequalities (LMI) technique, some sufficient conditions for the existence ofH∞robust controller are presented in terms of LMI dependent on the upper bound of time delays. The upper bound of time-delay and minimizedH∞performance index can be obtained by using convex optimization such that the system can be stabilized and for all time delays whose sizes are not larger than the bound. Finally, the effectiveness of the proposed controller is demonstrated through simulation example.

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

2011 ◽  
Vol 20 (04) ◽  
pp. 657-666
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Estimation Error ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
State Estimator ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals RobustH∞Filtering for Uncertain Neutral Stochastic Systems with Markovian Jumping Parameters and Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Yajun Li ◽  
Zhaowen Huang
Keyword(s):  
Time Delay ◽  
Stochastic Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Stochastically Stable ◽  
Neutral Stochastic Systems ◽  
Error System ◽  
Delay Dependent

This paper deals with the robustH∞filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribedH∞performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.

scholarly journals Nonfragile Quantized Dissipative Filter for Nonlinear Networked Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Kewang Huang ◽  
Jianfeng Wang ◽  
Feng Pan
Keyword(s):  
Time Delays ◽  
Sufficient Conditions ◽  
Networked Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Parameter Perturbation ◽  
Filter Parameter ◽  
Performance Requirements ◽  
One Step ◽  
Error System

To address the problem of filter parameter perturbation in nonlinear networked systems, a nonfragile quantized dissipative filter is designed by considering the coexistence of random one-step time delay, multipacket losses, and quantization error. We acquired the sufficient conditions for the existence of filter by choosing appropriate Lyapunov function as well as utilizing linear matrix inequality. Furthermore, we obtained the parameter expressions of the designed filter. The designed filter could meet the performance requirements of stability and dissipativity for the filter error system under the condition of allowed time delays, packet loss probability, and quantization density. The effectiveness of the designed filter is verified by numerical simulation.

Nonlinear H∞ Synchronization of Chaotic Lur'e Systems

1997 ◽  
Vol 07 (06) ◽  
pp. 1323-1335 ◽  
Author(s):  
J. A. K. Suykens ◽  
J. Vandewalle ◽  
L. O. Chua
Keyword(s):  
Tracking Error ◽  
Feedback Mechanism ◽  
Channel Noise ◽  
Lur’E Systems ◽  
Synchronization Problem ◽  
Chaotic Lur’E Systems ◽  
Feedback Matrix ◽  
System Theoretical Approach ◽  
Field Modulation ◽  
Synchronization Scheme

In this paper a master-slave synchronization scheme for Lur'e systems is investigated, which consists of vector field modulation by means of the message signal. Using a full state error feedback mechanism and formulating the synchronization problem within the standard plant framework of modern control theory, it is shown how the original message can be recovered for a class of binary-valued continuous time reference inputs or message signals. Input/output properties of the synchronization scheme are analyzed using the system-theoretical approach of dissipativity with a quadratic storage function and a supply rate of finite L2-gain. The feedback matrix is designed such that the influence of the exogenous input on a tracking error is minimized, corresponding to a so-called nonlinear H∞ synchronization scheme. Channel noise is taken into account in the design. The method is illustrated on Chua's circuit and an n-double scroll circuit.

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