Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control

Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control

This paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the cons...

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Main Authors: Xiaoman Liu, Haiyang Zhang, Tao Wu, Jinlong Shu
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/3956549
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spelling doaj-31969d62464b4485adf55fa6698549692020-11-25T02:57:45ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/39565493956549Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive ControlXiaoman Liu0Haiyang Zhang1Tao Wu2Jinlong Shu3School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, ChinaSchool of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, ChinaDepartment of Mathematics, Southeast University, Nanjing 210096, ChinaSchool of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, ChinaThis paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the conservativeness of stability criteria. To further save control cost, we introduce a sample-based Adaptive Event-triggered Impulsive Control (AEIC) scheme, in which the trigger threshold is adaptively varied with the sampled state. By fully considering the information about sampled state, TDs, and Markov jump parameters, a suitable Lyapunov–Krasovskii functional is constructed. With the virtue of FMEII and AEIC scheme, some novel stabilization criteria are presented in the form of linear matrix inequalities. At last, two numerical examples are given to show the validity of the obtained results.http://dx.doi.org/10.1155/2020/3956549
collection DOAJ
language English
format Article
sources DOAJ
author Xiaoman Liu
Haiyang Zhang
Tao Wu
Jinlong Shu
spellingShingle Xiaoman Liu
Haiyang Zhang
Tao Wu
Jinlong Shu
Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control
Complexity
author_facet Xiaoman Liu
Haiyang Zhang
Tao Wu
Jinlong Shu
author_sort Xiaoman Liu
title Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control
title_short Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control
title_full Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control
title_fullStr Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control
title_full_unstemmed Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control
title_sort stochastic exponential stabilization for markov jump neural networks with time-varying delays via adaptive event-triggered impulsive control
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
description This paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the conservativeness of stability criteria. To further save control cost, we introduce a sample-based Adaptive Event-triggered Impulsive Control (AEIC) scheme, in which the trigger threshold is adaptively varied with the sampled state. By fully considering the information about sampled state, TDs, and Markov jump parameters, a suitable Lyapunov–Krasovskii functional is constructed. With the virtue of FMEII and AEIC scheme, some novel stabilization criteria are presented in the form of linear matrix inequalities. At last, two numerical examples are given to show the validity of the obtained results.
url http://dx.doi.org/10.1155/2020/3956549
work_keys_str_mv AT xiaomanliu stochasticexponentialstabilizationformarkovjumpneuralnetworkswithtimevaryingdelaysviaadaptiveeventtriggeredimpulsivecontrol
AT haiyangzhang stochasticexponentialstabilizationformarkovjumpneuralnetworkswithtimevaryingdelaysviaadaptiveeventtriggeredimpulsivecontrol
AT taowu stochasticexponentialstabilizationformarkovjumpneuralnetworkswithtimevaryingdelaysviaadaptiveeventtriggeredimpulsivecontrol
AT jinlongshu stochasticexponentialstabilizationformarkovjumpneuralnetworkswithtimevaryingdelaysviaadaptiveeventtriggeredimpulsivecontrol
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