Stability analysis of hybrid neural networks with impulsive time window

The urgent problem with impulsive moments cannot be determined in advance brings new challenges beyond the conventional impulsive systems theory. In order to solve this problem, in this paper, a novel class of system with impulsive time window is proposed. Different from the conventional impulsive control strategies, the main characteristic of the impulsive time window is that impulse occurs in a random manner. Moreover, for the importance of the hybrid neural networks, using switching Lyapunov functions and a generalized Hanlanay inequality, some general criteria for asymptotic and exponential stability of the hybrid neural networks with impulsive time window are established. Finally, some simulations are provided to further illustrate the effectiveness of the results.

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Lyapunov Control of Quantum Systems with Impulsive Control Fields

The Scientific World JOURNAL ◽

10.1155/2013/814080 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

Wei Yang ◽

Jitao Sun

Keyword(s):

Lyapunov Functions ◽

Control Method ◽

Impulsive Control ◽

Sufficient Conditions ◽

Quantum Systems ◽

Impulsive Systems ◽

Finite Dimensional ◽

Lyapunov Control ◽

Control Of Quantum Systems ◽

Invariant Principle

We investigate the Lyapunov control of finite-dimensional quantum systems with impulsive control fields, where the studied quantum systems are governed by the Schrödinger equation. By three different Lyapunov functions and the invariant principle of impulsive systems, we study the convergence of quantum systems with impulsive control fields and propose new results for the mentioned quantum systems in the form of sufficient conditions. Two numerical simulations are presented to illustrate the effectiveness of the proposed control method.

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Linear impulsive control system with impulse time windows

Journal of Vibration and Control ◽

10.1177/1077546315575465 ◽

2016 ◽

Vol 23 (1) ◽

pp. 111-118 ◽

Cited By ~ 17

Author(s):

Yuming Feng ◽

Junzhi Yu ◽

Chuandong Li ◽

Tingwen Huang ◽

Hangjun Che

Keyword(s):

Impulsive Control ◽

Time Window ◽

Time Windows ◽

Practical Importance ◽

Fixed Time ◽

Small Time ◽

Time Interval ◽

Impulsive Systems ◽

Impulse Time Windows ◽

System States

We formulate the linear impulsive control systems with impulse time windows. Different from the most impulsive systems where the impulses occur at fixed time or when the system states hit a certain hyperplane, the impulse time in the presented systems might be uncertain, but limited to a small time interval, i.e. a time window. Compared with the existing impulsive systems, the systems with impulse time windows is of practical importance. We then study the asymptotic stability of the case of linear systems and obtain several stability criteria. Numerical examples are given to verify the effectiveness of the theoretical results.

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Quasi-Synchronization of Nonidentical Fractional-Order Memristive Neural Networks via Impulsive Control

Discrete Dynamics in Nature and Society ◽

10.1155/2021/6659063 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Ruihan Chen ◽

Tianfeng Zhao

Keyword(s):

Neural Networks ◽

Laplace Transform ◽

Fractional Order ◽

Convergence Rates ◽

Impulsive Control ◽

Memristive Neural Networks ◽

Impulsive Systems ◽

The Laplace Transform ◽

Average Impulsive Interval

This paper investigates the quasi-synchronization of nonidentical fractional-order memristive neural networks (FMNNs) via impulsive control. Based on a newly provided fractional-order impulsive systems comparison lemma, the average impulsive interval definition, and the Laplace transform, some quasi-synchronization conditions are obtained with fractional order 0 < α < 1 . In addition, the error convergence rates and error boundary are also obtained. Finally, one simulation example is presented to show the validity of our results.

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Finite-Time Lyapunov Functions and Impulsive Control Design

Complexity ◽

10.1155/2020/5179752 ◽

2020 ◽

Vol 2020 ◽

pp. 1-9

Author(s):

Huijuan Li ◽

Qingxia Ma

Keyword(s):

Finite Time ◽

Lyapunov Functions ◽

Lorenz System ◽

Impulsive Control ◽

Sufficient Conditions ◽

Impulsive System ◽

Impulsive Systems ◽

Lyapunov Theorem ◽

The Lorenz System ◽

The Stability

In this paper, we introduce finite-time Lyapunov functions for impulsive systems. The relaxed sufficient conditions for asymptotic stability of an equilibrium of an impulsive system are given via finite-time Lyapunov functions. A converse finite-time Lyapunov theorem for controlling the impulsive system is proposed. Three examples are presented to show how to analyze the stability of an equilibrium of the considered impulsive system via finite-time Lyapunov functions. Furthermore, according to the results, we design an impulsive controller for a chaotic system modified from the Lorenz system.

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