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Ju H Park - One of the best experts on this subject based on the ideXlab platform.
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a new approach to stabilization of chaotic systems with nonfragile fuzzy proportional retarded sampled Data control
IEEE Transactions on Systems Man and Cybernetics, 2019Co-Authors: Ruimei Zhang, Ju H Park, Yajuan Liu, Deqiang Zeng, Shouming ZhongAbstract:This paper is concerned with the problem of stabilization of chaotic systems via nonfragile fuzzy proportional retarded sampled-Data control. Compared with existing sampled-Data control schemes, a more practical nonfragile fuzzy proportional retarded sampled-Data Controller is designed, which involves not only a signal transmission delay but also uncertainties. Based on the Wirtinger inequality, a new discontinuous Lyapunov–Krasovskii functional (LKF), namely, Wirtinger-inequality-based time-dependent discontinuous (WIBTDD) LKF, is the first time to be proposed for sampled-Data systems. With the WIBTDD LKF approach and employing the developed estimation technique, a less conservative stabilization criterion is established. The desired fuzzy proportional retarded sampled-Data Controller can be obtained by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.
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robust h stabilization for t s fuzzy systems with time varying delays and memory sampled Data control
Applied Mathematics and Computation, 2019Co-Authors: Yanpen Shi, Ju H Park, Changchun HuaAbstract:Abstract In this paper, we address the robust H ∞ stabilization for T-S fuzzy systems with time-varying delays based on memory sampled-Data control. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices proposed in the LKF are not necessarily positive definite. By using the LKF and Free-Matrix-Based (FMB) integral inequality, some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an H ∞ norm bound. Then, the memory sampled-Data Controller can be derived by solving a group of linear matrix inequalities (LMIs) with the maximal sampling period. Finally, a numerical example is given to demonstrate the benefits and the superiority of the approach proposed.
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new methods of fuzzy sampled Data control for stabilization of chaotic systems
IEEE Transactions on Systems Man and Cybernetics, 2018Co-Authors: Tae H Lee, Ju H ParkAbstract:This paper focuses on developing new design methods of the sampled-Data Controller for chaotic systems which are represented as Takagi–Sugeno (T–S) fuzzy models. Two novel approaches, sampling-instant-to-present-time fragmentation and free-matrix-based time-dependent discontinuous Lyapunov approach, are proposed for the first time. Based on the two new approaches, the T–S fuzzy sampled-Data Controller is designed for stabilization of chaotic systems under large sampling period. The superiority of proposed results is shown by a numerical example.
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further results on stabilization of chaotic systems based on fuzzy memory sampled Data control
IEEE Transactions on Fuzzy Systems, 2018Co-Authors: Ju H ParkAbstract:This note investigates sampled-Data control for chaotic systems. A memory sampled-Data control scheme that involves a constant signal transmission delay is employed for the first time to tackle the stabilization problem for Takagi–Sugeno fuzzy systems. The advantage of the constructed Lyapunov functional lies in the fact that it is neither necessarily positive on sampling intervals nor necessarily continuous at sampling instants. By introducing a modified Lyapunov functional that involves the state of a constant signal transmission delay, a delay-dependent stability criterion is derived so that the closed-loop system is asymptotically stable. The desired sampled-Data Controller can be achieved by solving a set of linear matrix inequalities. Compared with the existing results, a larger sampling period is obtained by this new approach. A simulation example is presented to illustrate the effectiveness and conservatism reduction of the proposed scheme.
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mixed h passive sampled Data synchronization control of complex dynamical networks with distributed coupling delay
Journal of The Franklin Institute-engineering and Applied Mathematics, 2017Co-Authors: Jing Wang, Hao Shen, Ju H ParkAbstract:Abstract This paper investigates the problem of the mixed H ∞ / passive sampled-Data synchronization control for complex dynamical networks (CDNs) with distributed coupling delay. The sampled interval is deemed as time-varying. The main purpose is to design a sampled-Data Controller so as to the synchronization error system (SES) is exponentially stable and satisfies a predefined H ∞ / passive performance index simultaneously. Some novel auxiliary function-based integral inequalities are applied to reduce the conservativeness of the presented results, and some effective synchronization criteria are addressed. The gains for the desired Controller can be designed by settling an optimization issue in view of the proposed criteria. Three examples are employed to demonstrate the less conservativeness and superiority of the addressed method.
Hongbing Zeng - One of the best experts on this subject based on the ideXlab platform.
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a new lyapunov functional approach to sampled Data synchronization control for delayed neural networks
Journal of The Franklin Institute-engineering and Applied Mathematics, 2018Co-Authors: Shenping Xiao, Honghai Lian, Hongbing Zeng, Kok Lay Teo, Xiaohu ZhangAbstract:Abstract This paper discusses the problem of synchronization for delayed neural networks using sampled-Data control. We introduce a new Lyapunov functional, called complete sampling-interval-dependent discontinuous Lyapunov functional, which can adequately capture sampling information on both intervals from r ( t − τ ¯ ) to r ( t k − τ ¯ ) and from r ( t − τ ¯ ) to r ( t k + 1 − τ ¯ ) . Based on this Lyapunov functional and an improved integral inequality, less conservative conditions are derived to ensure the stability of the synchronization error system, leading to the fact that the drive neural network is synchronized with the response neural network. The desired sampled-Data Controller is designed in terms of solutions to linear matrix inequalities. A numerical example is provided to demonstrate that the proposed approaches are effective and superior to some existing ones in the literature.
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sampled Data synchronization control for chaotic neural networks subject to actuator saturation
Neurocomputing, 2017Co-Authors: Hongbing Zeng, Yong He, Honglei Xu, Wei WangAbstract:Abstract In this paper, the sampled-Data control is applied to synchronize chaotic neural networks subject to actuator saturation. By employing a time-dependent Lyapunov functional that captures the characteristic information of actual sampling pattern, we derive a local stability condition for the synchronization error systems. By this condition, we design a sampled-Data Controller to regionally synchronize the drive neural networks and response neural networks subject to actuator saturation. Moreover, an optimization method is given to design the desired sampled-Data Controller such that the set of admissible initial conditions is maximized. A numerical example is given to demonstrate the effectiveness and merits of the proposed design technique.
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free matrix based time dependent discontinuous lyapunov functional for synchronization of delayed neural networks with sampled Data control
Chinese Physics B, 2017Co-Authors: Wei Wang, Hongbing Zeng, Kok Lay TeoAbstract:This paper is concerned with the synchronization of delayed neural networks via sampled-Data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-Data Controller can be obtained through the use of the linear matrix inequality (LMI) technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.
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further results on sampled Data control for master slave synchronization of chaotic lur e systems with time delay
Nonlinear Dynamics, 2015Co-Authors: Shenping Xiao, Hongbing Zeng, Ju H Park, Yajuan LiuAbstract:This paper is concerned with the problem of sampled-Data control for master–slave synchronization of chaotic Lur’e systems with time delay. The sampling periods are assumed to be arbitrary but bounded. A new Lyapunov functional is constructed, in which the information on the nonlinear function and the actual sampling pattern have been taken fully into account. By employing the Lyapunov functional and a tighter bound technique to estimate the derivative of the Lyapunov functional, a less conservative exponential synchronization criterion is established by analyzing the corresponding synchronization error systems. Furthermore, the derived condition is employed to design a sampled-Data Controller. The desired Controller gain matrix can be obtained by means of the linear matrix inequality approach. Simulations are provided to show the effectiveness and the advantages of the proposed approach.
Jian Chu - One of the best experts on this subject based on the ideXlab platform.
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local synchronization of chaotic neural networks with sampled Data and saturating actuators
IEEE Transactions on Systems Man and Cybernetics, 2014Co-Authors: Peng Shi, Jian ChuAbstract:This paper investigates the problem of local synchronization of chaotic neural networks with sampled-Data and actuator saturation. A new time-dependent Lyapunov functional is proposed for the synchronization error systems. The advantage of the constructed Lyapunov functional lies in the fact that it is positive definite at sampling times but not necessarily between sampling times, and makes full use of the available information about the actual sampling pattern. A local stability condition of the synchronization error systems is derived, based on which a sampled-Data Controller with respect to the actuator saturation is designed to ensure that the master neural networks and slave neural networks are locally asymptotically synchronous. Two optimization problems are provided to compute the desired sampled-Data Controller with the aim of enlarging the set of admissible initial conditions or the admissible sampling upper bound ensuring the local synchronization of the considered chaotic neural networks. A numerical example is used to demonstrate the effectiveness of the proposed design technique.
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sampled Data synchronization of chaotic lur e systems with time delays
IEEE Transactions on Neural Networks, 2013Co-Authors: Peng Shi, Jian ChuAbstract:This paper studies the problem of sampled-Data control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems with time delays. It is assumed that the sampling periods are arbitrarily varying but bounded. In order to take full advantage of the available information about the actual sampling pattern, a novel Lyapunov functional is proposed, which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals. Based on the Lyapunov functional, an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems. The desired sampled-Data Controller is designed by a linear matrix inequality approach. The effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of Chua's circuit and neural network.
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exponential synchronization of neural networks with discrete and distributed delays under time varying sampling
IEEE Transactions on Neural Networks, 2012Co-Authors: Peng Shi, Jian ChuAbstract:This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-Data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-Data Controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.
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discontinuous lyapunov functional approach to synchronization of time delay neural networks using sampled Data
Nonlinear Dynamics, 2012Co-Authors: Ju H Park, Jian ChuAbstract:This paper investigates the synchronization problem of neural networks with time-varying delay under sampled-Data control in the presence of a constant input delay. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The design method of the desired sampled-Data Controller is also proposed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.
R Rakkiyappan - One of the best experts on this subject based on the ideXlab platform.
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stochastic sampled Data control for synchronization of complex dynamical networks with control packet loss and additive time varying delays
Neural Networks, 2015Co-Authors: R Rakkiyappan, N Sakthivel, Jinde CaoAbstract:This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-Data Controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-Data Controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.
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synchronization of neural networks with control packet loss and time varying delay via stochastic sampled Data Controller
IEEE Transactions on Neural Networks, 2015Co-Authors: R Rakkiyappan, S Dharani, Jinde CaoAbstract:This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-Data Controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the Controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov–Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.
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synchronization of reaction diffusion neural networks with time varying delays via stochastic sampled Data Controller
Nonlinear Dynamics, 2015Co-Authors: R Rakkiyappan, S Dharani, Quanxin ZhuAbstract:This paper discusses the synchronization problem for a class of reaction–diffusion neural networks with Dirichlet boundary conditions. Unlike other studies, a sampled-Data Controller with stochastic sampling is designed in order to synchronize the concerned neural networks with reaction–diffusion terms and time-varying delays, where $$m$$ sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. A novel discontinuous Lyapunov–Krasovskii functional with triple integral terms is introduced based on the extended Wirtinger’s inequality. Using Jensen’s inequality and reciprocally convex technique in deriving the upper bound for the derivative of the Lyapunov–Krasovskii functional, some new synchronization criteria are obtained in terms of linear matrix inequalities. Numerical examples are provided in order to show the effectiveness of the proposed theoretical results.
Jinde Cao - One of the best experts on this subject based on the ideXlab platform.
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stochastic sampled Data control for synchronization of complex dynamical networks with control packet loss and additive time varying delays
Neural Networks, 2015Co-Authors: R Rakkiyappan, N Sakthivel, Jinde CaoAbstract:This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-Data Controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-Data Controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.
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synchronization of neural networks with control packet loss and time varying delay via stochastic sampled Data Controller
IEEE Transactions on Neural Networks, 2015Co-Authors: R Rakkiyappan, S Dharani, Jinde CaoAbstract:This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-Data Controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the Controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov–Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.
