Synchronization criteria of chaotic Lur׳e systems with delayed feedback PD control

Liu, Yajuan; Lee, Sang Moon

doi:10.1016/j.neucom.2015.12.058

Cited by 23 publications

(14 citation statements)

References 37 publications

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“…Remark It should be noted that the memory PD asynchronous control scheme can play a key role in achieving the better control goals such as overshoot reduction in the responses, sensitivity reduction to parameter variations, and performance improvement of the control systems. () The reason is that the derivative controls can speed the system response to enhance stability. In addition, the randomly occurring uncertainties and randomly occurring gain fluctuations have been also taken into full consideration.…”

Section: Resultsmentioning

confidence: 99%

“…Remark In addition, new integral inequalities in Lemma have not been considered earlier for uncertain CLNSs in the literature so far. () Moreover, the advantage of the dealing techniques lies in taking full account of the relationship of state‐augmented vectors, eg,

\int_{t - normalβ d}^{t} ė^{T} false(s false) R_{3} ė false(s false) d s

, e ( t ), e ( t −β d ),

\int_{t - normalβ d}^{t} e false(s false) d s

\int_{- normalβ d}^{0} \int_{t + normalθ}^{t} e false(s false) d s d normalθ

, and

\int_{- normalβ d}^{0} \int_{normalθ}^{0} \int_{t + normalλ}^{t} e false(s false) d s d normalλ d normalθ

, which reduce further the conservatism of synchronization conditions. ()…”

Section: Resultsmentioning

confidence: 99%

“…The main contributions of this paper are listed as follows. First, different from the proposed methods of the literatures,() an appropriate LKF with flexible integral intervals is chosen by getting the utmost out of the additional derivative state term and multiple integral terms. Second, to develop less conservative asynchronous conditions for the uncertain error systems, novelly tighter upper bound integral inequalities in the work of Chen et al were employed to estimate the derivative of the constructed LKF because they can provide more accurate bounds with more orthogonal polynomials considered.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

Shi

Tang

Zhong

et al. 2017

Intl J Robust & Nonlinear

198

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This paper proposes a novel nonfragile robust asynchronous control scheme for master-slave uncertain chaotic Lurie network systems with randomly occurring time-varying parameter uncertainties and controller gain fluctuation. The asynchronous phenomenon occurs between the system modes and the controller modes. In order to consider a more realistic situation in designing a reliable proportional-derivative controller, Bernoulli stochastic process and memory feedback are introduced to the concept of nonlinear control system. First, by taking full advantage of the additional derivative state term and variable multiple integral terms, a newly augmented Lyapunov-Krasovskii functional is constructed via an adjustable parameter. Second, based on new integral inequalities including almost all of the existing integral inequalities, which can produce more accurate bounds with more orthogonal polynomials considered, less conservative synchronization criteria are obtained. Third, a desired nonfragile estimator controller is achieved under the aforementioned methods.Finally, 4 numerical simulation examples of Chua's circuit and 3-cell cellular neural network with multiscroll chaotic attractors are presented to illustrate the effectiveness and advantages of the proposed theoretical results.

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Section: Resultsmentioning

confidence: 99%

\int_{t - normalβ d}^{t} ė^{T} false(s false) R_{3} ė false(s false) d s

, e ( t ), e ( t −β d ),

\int_{t - normalβ d}^{t} e false(s false) d s

\int_{- normalβ d}^{0} \int_{t + normalθ}^{t} e false(s false) d s d normalθ

, and

\int_{- normalβ d}^{0} \int_{normalθ}^{0} \int_{t + normalλ}^{t} e false(s false) d s d normalλ d normalθ

, which reduce further the conservatism of synchronization conditions. ()…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

Shi

Tang

Zhong

et al. 2017

Intl J Robust & Nonlinear

198

View full text Add to dashboard Cite

show abstract

“…Substituting (12) in (4) and assuming an accurate estimation of the total disturbance, the controlled slave system becomes:…”

Section: Controller Designmentioning

confidence: 99%

“…The synchronization between non-autonomous hyperchaotic systems viz., Liu and 4D hyperchaotic non-autonomous systems with parametric uncertainties using active control method was reported in [11]. The global asymptotical synchronization of chaotic Lur'e systems by using a delayed feedback proportional-derivative (PD) control scheme was reported in [12]. Based on a high order sliding-mode observer-identifier and a feedback state controller, the reducedorder synchronization problem of two chaotic systems with different dimension and relative degree was studied in [13].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Chaotic Systems via Active Disturbance Rejection Control

Khadra¹

2017

ICA

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This paper presents the use of active disturbance rejection control method (ADRC) to synchronize two different chaotic systems. The master system and slave systems have uncertainties and external disturbances. The numerical results are presented for the synchronization between the Duffing-Holmes system and the van der pol system. The numerical results presented show the effectiveness of the proposed method.

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Synchronization Stability Criteria for Lur’e Systems via Delay-Product-Type Functional Method

Liu

et al. 2022

Circuits Syst Signal Process

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Synchronization criteria of chaotic Lur׳e systems with delayed feedback PD control

Cited by 23 publications

References 37 publications

Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

Nonfragile asynchronous control for uncertain chaotic Lurie network systems with Bernoulli stochastic process

Synchronization of Chaotic Systems via Active Disturbance Rejection Control

Synchronization Stability Criteria for Lur’e Systems via Delay-Product-Type Functional Method

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