Synchronization Criterion for Lur’e Systems via Delayed PD Controller

Ji, D. H.; Park, Ju H.; Lee, Sang Moon; Koo, J. H.; Won, Sangchul

doi:10.1007/s10957-010-9723-0

Cited by 16 publications

(12 citation statements)

References 24 publications

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“…Then, adding the left-hand side of (30) and (31) tȯ V (t), we obtain from (16), (17), (19), (21), (24), (25), and (29) that for t ∈ [t k , t k+1 ),…”

Section: Resultsmentioning

confidence: 99%

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Further results on sampled-data control for master–slave synchronization of chaotic Lur’e systems with time delay

et al. 2015

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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.

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“…Then, adding the left-hand side of (30) and (31) tȯ V (t), we obtain from (16), (17), (19), (21), (24), (25), and (29) that for t ∈ [t k , t k+1 ),…”

Section: Resultsmentioning

confidence: 99%

“…These results were extended to the fault-tolerant master-slave synchronization of Lur'e systems in [16]. The master-slave synchronization problem has been investigated for Lur'e systems via delayed PD controller in [17].…”

Section: Introductionmentioning

confidence: 99%

Further results on sampled-data control for master–slave synchronization of chaotic Lur’e systems with time delay

et al. 2015

Self Cite

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“…In the following theorem, the finite-time convergence and stability of the synchronization error system (6) are proved. (6) is controlled by the control laws (13) with the update laws (14), then the error system's trajectories will converge to zero in the finite time T , determined by…”

Section: Design Of a Robust Adaptive Finite-time Controllermentioning

confidence: 99%

“…Since the control signals in (13) include the terms e i / e 2 and sgn(e i ) = |e i |/e i , i = 1, 2, 3, 4, the undesirable chattering phenomenon may occur. In order to remove the chattering, these terms are modified as e i /( e 2 + ε) and |e i |/(e i + ε), i = 1, 2, 3, 4, respectively, where ε > 0 is a sufficiently small constant [20,21].…”

Section: Remarkmentioning

confidence: 99%

“…The master-slave (drive-response) configuration is a basic framework for chaos synchronization, where the slave system's trajectories should track the master system's trajectories. Since the pioneering work by Pecora and Carroll in 1990 [2], synchronization of chaotic systems has received considerable attention in the last decade and several useful control techniques, such as sliding mode control [3,4], finitetime control [5], passive control [6], H ∞ approach [7], PID control [8], fuzzy logic control [9], and delayed feedback control [10][11][12][13], have been successfully applied to realize chaos synchronization.…”

Section: Introductionmentioning

confidence: 99%

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Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

Aghababa

2011

Nonlinear Dyn

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This paper solves the problem of robust synchronization of nonlinear chaotic gyrostat systems in a given finite time. The parameters of both master and slave chaotic gyrostat systems are assumed to be unknown in advance. In addition, the gyrostat systems are disturbed by unknown model uncertainties and external disturbances. Suitable update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in finite time. The precise value of the convergence time is given. A numerical simulation demonstrates the applicability and efficiency of the proposed finite-time synchronization strategy.

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Synchronization Criterion and Control Scheme for Lur'e Type Complex Dynamical Networks with Switching Topology and Coupling Time‐Varying Delay

Zhang¹,

Li²,

Yang³

et al. 2014

Asian Journal of Control

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In this paper, the synchronization problem is addressed in the context of Lur'e type complex switched network (CSN) with coupling time-varying delay in which every node is a Lur'e system. Based on the Lyapunov-Krasovskii theory and linear matrix inequality (LMI) technique, a delay-dependent synchronization criterion and a decentralized state feedback dynamic controller for synchronization of CSNs have been proposed. By choosing a common Lyapunov-Krasovskii functional and using the combined reciprocal convex technique, some previously ignored terms can be reconsidered and less conservative conditions can be obtained. In addition, by using an eigenvalue-decoupling method and convex optimization theory, highdimension LMIs are decoupled into a set of low-dimension ones and the computation complexity of the criterion can be significantly reduced. The effectiveness and applicability of the suggested control solution is verified and assessed through the analysis for two numerical examples.

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Synchronization Criterion for Lur’e Systems via Delayed PD Controller

Cited by 16 publications

References 24 publications

Further results on sampled-data control for master–slave synchronization of chaotic Lur’e systems with time delay

Further results on sampled-data control for master–slave synchronization of chaotic Lur’e systems with time delay

Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

Synchronization Criterion and Control Scheme for Lur'e Type Complex Dynamical Networks with Switching Topology and Coupling Time‐Varying Delay

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