State feedback synchronization control of coronary artery chaos system with interval time-varying delay

Wu, Weixin; Zhao, Zhanshan; Zhang, Jing; Sun, Liankun

doi:10.1007/s11071-016-3151-0

Cited by 25 publications

(25 citation statements)

References 38 publications

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“…Assumption 3. The synchronization error system (7) satisfies the H ∞ performance index with the zero initial condition, if there exists [17,23,24]…”

Section: Assumptionmentioning

confidence: 99%

“…The section exhibits the numerical simulations of coronary artery system to validate the presented method. According to the descriptions in (1)-(4), the system matrices are listed as follows [3,[15][16][17]…”

Section: Simulationmentioning

confidence: 99%

“…In 2015, without knowing the disturbance boundary, [16] designed a high-order sliding mode adaptive controller for coronary artery chaos synchronization, which can effectively alleviate the chattering effect. In 2017, considering the external disturbance and input control delay, the state feedback synchronization control for coronary artery chaos system was investigated by using a delay-partitioning approach [17].…”

Section: Introductionmentioning

confidence: 99%

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Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Zhao

Zhang

et al. 2018

Asian Journal of Control

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The paper investigates the observer-based H ∞ synchronization for coronary artery time-delay system under the state immeasurement and external uncertainty. A Luenberger-like state observer, the observation system, is designed to realize the state reconstruction of the master system. Based on the Lyapunov stability theory and Lyapunov-Krasovskii functional (LKF), the observer-based synchronization control condition is derived for a coronary artery system subjected to the external uncertainty bounded by L 2 norm. By introducing the delay-interval bounds and delay-derivative limits in LKF, the time-delays are handled by the delay-range-dependent strategy. The tighter upper bound of inequality can be obtained to reduce the conservation by employing further improved result of Jensen inequality and reciprocally convex approach. Furthermore, a decoupling technique is utilized to render the separate and simple controller and observer synthesis condition, which can be further solved by applying the cone complementary linearization approach respectively. Numerical simulations are listed to exhibit the effectiveness of the presented methodology.

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“…Assumption 3. The synchronization error system (7) satisfies the H ∞ performance index with the zero initial condition, if there exists [17,23,24]…”

Section: Assumptionmentioning

confidence: 99%

Section: Simulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Zhao

Zhang

et al. 2018

Asian Journal of Control

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“…Many practical engineering problems involving chaos require control techniques to convert chaotic attractors into stable periodic orbits. Since the pioneering work of Ott et al [9], numerous methods for the control of chaos have been devised [10][11][12][13][14][15][16][17][18][19]. Improving the performance of a controlled magnetic bearing system and/or eliminating chatter behavior require the conversion of chaotic behavior into periodic motion.…”

Section: Introduction and System Descriptionmentioning

confidence: 99%

Nonlinear Dynamics and Suppressing Chaos in Magnetic Bearing System

Chang

2020

Mathematical Problems in Engineering

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A nonlinear mathematical model of a magnetic bearing system has been obtained by applying a modified conventional identification technique based on the principle of harmonic balance. In this study, we examined the rich nonlinear dynamics of a magnetic bearing system with closed-loop control using phase portraits, Poincaré maps, and frequency spectra. The resulting bifurcation diagram can be used to evaluate the operational range of systems employing nonlinear actuators. Estimates of the largest Lyapunov exponent based on the properties of synchronization revealed the occurrence of chatter vibration indicative of chaotic motion. Various control methods, such as the state feedback control and the injection of dither signals, were then used to quench the chaotic behavior.

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“…To solve the problem, the literature [21] put forward the state feedback controller of the CACS with input time-varying delay and external disturbances. In order to reduce conservatism, the literature [22] accomplished the synchronization control of uncertain CACS under interval time-varying delay through delay-partitioning method.…”

Section: Introductionmentioning

confidence: 99%

Synchronization Control Design Based on Wirtinger Inequality for Uncertain Coronary Artery Time-Delay System With Input Saturation

Zhao

Wang

et al. 2019

IEEE Access

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This paper focuses on the synchronization of uncertain coronary artery chaos systems (CACSs) with the state and input time-varying delays under input saturation. First, the stability of the closed-loop system is established to ensure the synchronization between the diseased and healthy CACSs under input saturation by utilizing the local sector condition and the Lyapunov-Krasovskii functional (LKF) method. The use of Wirtinger inequality and the reciprocally convex method further reduces the conservatism. Second, by making use of the cone complementary linearization approach to deal with nonlinear terms, we obtained a state feedback controller. Finally, a robust state feedback controller is formulated to achieve the synchronization of the CACS under disturbances bounded by L 2 norm. The simulation results of the CACS synchronization are presented to demonstrate the effectiveness of the derived results, which provides a certain theoretical basis for curing diseases related to the coronary artery vessel.

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State feedback synchronization control of coronary artery chaos system with interval time-varying delay

Cited by 25 publications

References 38 publications

Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Nonlinear Dynamics and Suppressing Chaos in Magnetic Bearing System

Synchronization Control Design Based on Wirtinger Inequality for Uncertain Coronary Artery Time-Delay System With Input Saturation

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State feedback synchronization control of coronary artery chaos system with interval time-varying delay

Cited by 25 publications

References 38 publications

Observer‐Based H∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Observer‐Based H∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Nonlinear Dynamics and Suppressing Chaos in Magnetic Bearing System

Synchronization Control Design Based on Wirtinger Inequality for Uncertain Coronary Artery Time-Delay System With Input Saturation

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Product

Resources

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Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System