Positivity and Stability of Fractional-Order Linear Time-Delay Systems

Hao, Yilin; Huang, Chengdai; Cao, Jinde; Liu, Heng

doi:10.1007/s11424-022-1018-7

Cited by 5 publications

(3 citation statements)

References 44 publications

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“…Fractional calculus is more accurate than integral calculus in describing the physical phenomena in engineering applications and more in line with engineering practice. Thus, fractional calculus has high research value in electronic circuits [14,15], electromagnetic waves [16,17], secure communication [18,19], image encryption [20] and other fields. Through the in-depth study of chaos, scholars have found that fractional calculus is an effective theory for the analysis and explanation of chaos.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Terminal Sliding-Mode Synchronization Control with Chattering Elimination for a Fractional-Order Chaotic System

Wang

2024

Fractal Fract

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In this paper, an adaptive terminal sliding-mode control (ATSMC) method is proposed for the synchronization of uncertain fractional-order chaotic systems with disturbances. According to the sliding-mode control theory, a non-singular sliding surface is constructed. To overcome the chattering problem of ATSMC, a smooth term is used in the controller. In order to reduce the estimation error of an uncertain parameter, adaptive laws are designed to adjust the amplitude of the continuous function. Based on the Lyapunov stability theory, a stability analysis of the error system is performed to ensure that the tracking error eventually converges to the origin. The effectiveness and applicability of the proposed control strategy are verified using the simulation results.

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Section: Introductionmentioning

confidence: 99%

Adaptive Terminal Sliding-Mode Synchronization Control with Chattering Elimination for a Fractional-Order Chaotic System

Wang

2024

Fractal Fract

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“…It is shown that FOC provides some attractive natures for nonlinear systems, such as memory and genetics. Thus, FOC is already a popular theme, especially in mathematical modeling, engineering, economics, and physics [1][2][3][4][5]. Meanwhile, it has become a very important tool, which attracts the attention and research of many scholars.…”

Section: Introductionmentioning

confidence: 99%

Stabilization of delayed fractional‐order T‐S fuzzy systems with input saturations and system uncertainties

Hao

Fang

Liu

2023

Asian Journal of Control

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By adopting the Takagi–Sugeno (T‐S) fuzzy theory, this paper focuses on the adaptive control of fractional‐order time‐delay systems involving unknown parameters and input saturations. T‐S fuzzy systems with “IF‐THEN” rules are employed to describe fractional‐order nonlinear systems. The influence of input saturation is handled by designing an auxiliary system. By using a norm conversion, the system's time‐delay term is converted into a non‐delayed form. Adaptive updating rules are devised to evaluate uncertainties of the system, and a new control approach is proposed. The devised controller can not only guarantee the boundedness of variables involved but also make state variables converge into a sufficiently small neighborhood of the origin, even in the presence of uncertainties, saturation functions, and system parameters. Finally, numerical studies are given to verify the correctness of the designed scheme.

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“…Simultaneously, as influenced by a number of other factors, the fractional-order linear system model takes into account the time delay problem in [15]. Complex networks usually have time delay [16,17]. Hence, it is of significant value to investigate the synchronization problem in complex networks with uncertainties and time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

Event‐triggered sampled‐data synchronization of complex networks with uncertain inner coupling and time‐varying delays

Yan,

Zhao,

Liu

et al. 2023

Asian Journal of Control

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This paper focuses on event‐triggered sampled‐data synchronization of uncertain complex networks with time‐varying coupled delays. First of all, a discrete event‐triggered sampled‐data control scheme is adopted, which not only makes the state of the system be monitored in discrete time, but also the sampling information is effectively transmitted. The proposed event‐triggered mechanism effectively prevents Zeno behavior. In addition, we also use some novel piecewise time‐dependent Lyapunov–Krasovskii and Wirtinger inequality to handle the time‐varying delays and parameter uncertainties of complex networks. Then, synchronization criteria are given for uncertain complex networks. Finally, the simulation results show that the control scheme can significantly reduce the number of transmitted signals while maintaining the uncertain complex networks synchronization.

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Positivity and Stability of Fractional-Order Linear Time-Delay Systems

Cited by 5 publications

References 44 publications

Adaptive Terminal Sliding-Mode Synchronization Control with Chattering Elimination for a Fractional-Order Chaotic System

Adaptive Terminal Sliding-Mode Synchronization Control with Chattering Elimination for a Fractional-Order Chaotic System

Stabilization of delayed fractional‐order T‐S fuzzy systems with input saturations and system uncertainties

Event‐triggered sampled‐data synchronization of complex networks with uncertain inner coupling and time‐varying delays

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