Finite-Time Stabilization of Delayed Memristive Neural Networks: Discontinuous State-Feedback and Adaptive Control Approach

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

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Global Finite-Time Stabilization Problem of Affine Nonlinear Systems with Unknown Functions

10.22541/au.162080174.40414616/v1 ◽

2021 ◽

Author(s):

Fujin Jia ◽

Junwei Lu ◽

Yong-Min Li ◽

Fangyuan Li

Keyword(s):

Nonlinear Systems ◽

Finite Time ◽

Control Algorithm ◽

Lyapunov Analysis ◽

Stabilization Problem ◽

Analysis Method ◽

Control Approach ◽

Affine Nonlinear Systems ◽

Simulation Results ◽

Finite Time Stabilization

In this paper, the global finite-time stabilization (FTS) of nonlinear systems with unknown functions (UFs) is studied. Firstly, in order to deal with UFs, a Lemma is proposed to avoid the Assumptions of UFs. Secondly, based on this Lemma, the control algorithm designed by using backstepping has no partial derivative of virtual controllers, so it avoids the “differential explosion” problem of backstepping. Thirdly, by using Lyapunov analysis method, backstepping and FTS method, a global FTS control algorithm of nonlinear systems with UFs is proposed. Finally, the feasibility of developed control approach is illustrated by the simulation results of a manipulator.

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Finite-time stabilization of complex-valued neural networks with proportional delays and inertial terms: A non-separation approach

Neural Networks ◽

10.1016/j.neunet.2022.01.005 ◽

2022 ◽

Author(s):

Changqing Long ◽

Guodong Zhang ◽

Zhigang Zeng ◽

Junhao Hu

Keyword(s):

Neural Networks ◽

Finite Time ◽

Proportional Delays ◽

Finite Time Stabilization ◽

Inertial Terms ◽

Complex Valued

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Synchronization of time-varying time delayed neutral-type neural networks for finite-time in complex field

Mathematical Modeling and Computing ◽

10.23939/mmc2021.03.486 ◽

2021 ◽

Vol 8 (3) ◽

pp. 486-498

Author(s):

N. Jayanthi ◽

◽

R. Santhakumari ◽

Keyword(s):

Neural Networks ◽

Finite Time ◽

State Feedback ◽

Neutral Type ◽

State Feedback Control ◽

Projective Synchronization ◽

Time Varying ◽

Master System ◽

Complex Valued ◽

Theoretical Results

This paper deals with the problem of finite-time projective synchronization for a class of neutral-type complex-valued neural networks (CVNNs) with time-varying delays. A simple state feedback control protocol is developed such that slave CVNNs can be projective synchronized with the master system in finite time. By employing inequalities technique and designing new Lyapunov--Krasovskii functionals, various novel and easily verifiable conditions are obtained to ensure the finite-time projective synchronization. It is found that the settling time can be explicitly calculated for the neutral-type CVNNs. Finally, two numerical simulation results are demonstrated to validate the theoretical results of this paper.

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