Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks

Hu, Cheng; Yu, Juan; Chen, Zhanheng; Jiang, Haijun; Huang, Tingwen

doi:10.1016/j.neunet.2017.02.001

Cited by 354 publications

(136 citation statements)

References 50 publications

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“…Lemma 3 (see [31]). Assume that there exists a continuous positive definite and radially unbounded function ( ( )) and its right directional derivative satisfies the differential inequality:̇( ( )) + ( ( )) + ( ( )) ≤ 0,…”

Section: Design Of Adaptive Fixed-time Terminal Sliding Mode Controllmentioning

confidence: 99%

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

Yang

2019

Mathematical Problems in Engineering

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In order to study the stability of the wind turbine drivetrain in further depth, we present a nonlinear relative rotation mathematical model considering the nonlinear time-varying stiffness and the nonlinear damping force. Meanwhile, the nonlinear dynamics of the model under combined harmonic excitation are studied in detail. And some interesting dynamic phenomena are observed visually. Furthermore, to suppress chaotic oscillation within bounded time independent of initial conditions, a novel adaptive fixed-time terminal sliding mode controller is proposed. The stability of the final closed loop system is guaranteed according to Lyapunov stability theory. Rigorous mathematical analyses are used to prove the validity of the presented approach. Finally, compared with the existing finite-time stability method, simulation results are given to highlight the effectiveness and superiority of the proposed method and verify the theoretical analyses.

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Section: Design Of Adaptive Fixed-time Terminal Sliding Mode Controllmentioning

confidence: 99%

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

Yang

2019

Mathematical Problems in Engineering

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“…In order to overcome these shortcomings, a new concept named fixed-time synchronization was firstly taken into account in [19]. Hints for future research on the fixed-time synchronization problem can be found in [20][21][22][23][24][25]. By designing a sliding mode controller, the fixed-time synchronization issue for complex dynamical networks was addressed in [21].…”

Section: Introductionmentioning

confidence: 99%

Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays

Zhao

2018

Adv Differ Equ

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This paper is concerned with the global fixed-time synchronization issue for semi-Markovian jumping neural networks with time-varying delays. A novel state-feedback controller, which includes integral terms and time-varying delay terms, is designed to realize the fixed-time synchronization goal between the drive system and the response system. By applying the Lyapunov functional approach and matrix inequality analysis technique, the fixed-time synchronization conditions are addressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the feasibility of the proposed control scheme and the validity of theoretical results.

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“…Compared with the finite-time control, the fixed-time control has the characteristic that the maximum adjustment time is not affected by the initial conditions. In view of many advantages of fixed-time control, the control method has been widely used in multiagent systems [25], aircraft systems [26], robot systems [27], neural network systems [28][29][30][31], and chaotic systems [32,33].…”

Section: Introductionmentioning

confidence: 99%

Fixed-Time Stability of the Hydraulic Turbine Governing System

Liu

Zhang

et al. 2018

Mathematical Problems in Engineering

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This paper studies the problem of fixed-time stability of hydraulic turbine governing system with the elastic water hammer nonlinear model. To control and improve the quality of hydraulic turbine governing system, a new fixed-time control strategy is proposed, which can stabilize the water turbine governing system within a fixed time. Compared with the finite-time control strategy where the convergence rate depends on the initial state, the settling time of the fixed-time control scheme can be adjusted to the required value regardless of the initial conditions. Finally, we numerically show that the fixed-time control is more effective than and superior to the finite-time control.

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Fixed-time stability of dynamical systems and fixed-time synchronization of coupled discontinuous neural networks

Cited by 354 publications

References 50 publications

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

Dynamical Analysis and Stabilization of Wind Turbine Drivetrain via Adaptive Fixed‐Time Terminal Sliding Mode Controller

Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays

Fixed-Time Stability of the Hydraulic Turbine Governing System

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