Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling

Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad

doi:10.1016/j.isatra.2014.09.007

Cited by 22 publications

(9 citation statements)

References 46 publications

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“…By application of the LPV approach, the error dynamics (5) is converted into an equivalent LPV representation, given by (13) and (14). This LPV-based transformation, in contrast to the conventional adaptive treatments [16,17] and [19,20], allows computation of a controller gain matrix, by relaxing adaptive terms, in the presence of additional constraints like input delay.…”

Section: Resultsmentioning

confidence: 99%

“…Theorem 1 provides a synchronization controller design criterion, by selection of an appropriate value of K , that depends on both the upper and the lower bounds of the input delay by using the LK functional and the LPV theories (see, for instance, [13][14][15] and [23][24][25][26][27] and references therein). Theorem 2 is more pragmatic because it allows computation of the controller gain K for delay-rangedependent synchronization of the master-slave systems under slope-restricted unknown input nonlinearity.…”

Section: Remarkmentioning

confidence: 99%

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Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

2015

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This article addresses the synchronization of nonlinear master-slave systems under input time-delay and sloperestricted input nonlinearity. The input nonlinearity is transformed into linear time-varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple-integral-based Lyapunov-Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay-range-dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope-restricted nonlinearity. Further, time-delays are treated using an advanced delay-range-dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems.

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Section: Resultsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

2015

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“…In order to reduce the negative impact of time delay, we need to reduce the conservatism of the system and improve the performance of the system; many researchers 2 Complexity have used the triple integral form of LKF to analyze the stability of various time-delay systems in recent years, such as Wirtinger-based integral inequality [24], Jensen's inequality [25], and Wirtinger-based double integral inequality [26], and explain its effectiveness in reducing the conservativeness of stability criteria. Due to the method of literature [26] can be applied directly in finding lower bound of double integral, such as ∫ − ∫̇( )( ) ( > 0), and the method of literature [24] can not be applied directly in solving it.…”

Section: Introductionmentioning

confidence: 99%

Improved T‐S Fuzzy Control for Uncertain Time‐Delay Coronary Artery System

et al. 2019

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This paper is based on the Takagi-Sugeno (T-S) fuzzy models to construct a coronary artery system (CAS) T-S fuzzy controller and considers the uncertainties of system state parameters in CAS. We propose the fuzzy model of CAS with uncertainties. By using T-S fuzzy model of CAS and the use of parallel distributed compensation (PDC) concept, the same fuzzy set is assigned to T-S fuzzy controller. Based on this, a PDC controller whose fuzzy rules correspond to the fuzzy model is designed. By constructing a suitable Lyapunov-Krasovskii function (LKF), the stability conditions of the linear matrix inequality (LMI) are exported. Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance.

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“…Recently, considering nonlinearly coupled chaotic systems, [30] proposed a state feedback controller to achieve synchronization. However, the input nonlinearity was not considered.…”

Section: Introductionmentioning

confidence: 99%

Robust Adaptive Output Feedback Control Scheme for Chaos Synchronization with Input Nonlinearity

Zhao

Zhang

et al. 2016

Journal of Control Science and Engineering

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This paper proposes a robust adaptive output feedback control strategy which can automatically regulate control gain for chaos synchronization. Chaotic systems with input nonlinearities, delayed nonlinear coupling, and external disturbance can achieve synchronization by applying this strategy. Utilizing Lyapunov method and LMI technique, the conditions ensuring chaos synchronization are obtained. Finally, simulations are given to show the effectiveness of our control strategy.

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Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling

Cited by 22 publications

References 46 publications

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

Improved T‐S Fuzzy Control for Uncertain Time‐Delay Coronary Artery System

Robust Adaptive Output Feedback Control Scheme for Chaos Synchronization with Input Nonlinearity

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