Globally exponential stabilization of neural networks with mixed time delays via impulsive control

Wei, Linna; Chen, Wu‐Hua; Huang, Guoquan

doi:10.1016/j.amc.2015.03.043

Cited by 13 publications

(5 citation statements)

References 47 publications

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“…The impulsive control, as a hybrid control approach, has attracted significant interest in many applications [29][30][31][32], since its control input is only imposed on the topological structure of systems at some discrete moments, which can dramatically decrease the quantity of transmitted information and control cost. Hence, a great many attractive results on the impulsive control of delayed neural networks have been presented in recent years [33][34][35][36]. However, there has been limited work on delayed complex-valued systems [37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties

Yin

Wang

2022

Mathematics

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This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs into real and imaginary parts, some stability criteria in terms of complex-valued linear matrix inequalities (LMIs) are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed. Moreover, a new impulsive differential inequality is applied to resolve the difficulties caused by the mixed time delays and delayed impulse effects. Finally, an illustrative example is provided to back up our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties

Yin

Wang

2022

Mathematics

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“…In the design of neural networks, the dynamical properties of networks, such as the stability of the networks, play important roles. And there have been many literatures on the stability of neural networks [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

“…For master-slave neural networks, some kind of control term can been added to the slave system in order to guarantee the synchronization between the master system and the slave system. There are many control strategies such as impulsive control [7][8][9]19,25], feedback control [10,28], intermittent control [11,12,15], sampled-data control [13,14] and so on to stabilize the RNNs. To be noted that the sampled-data control drastically reduces the amount of transmitted information and increases the efficiency of bandwidth usage, because its' control signals are kept constant during the sampling period and are allowed to change only at the sampling instant.…”

Section: Introductionmentioning

confidence: 99%

Stability of Inertial Neural Network with Time-Varying Delays Via Sampled-Data Control

Wang

2018

Neural Process Lett

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In this paper, the stability problem is studied for inertial neural network with time-varying delays. The sampled-data control method is employed for the system design. First, by choosing a proper variable substitution, the original system is transformed into first-order differential equations. Then, an input delay approach is applied to deal with the stability of sampling system. Based on the Lyapunov function method, several sufficient conditions are derived to guarantee the global stability of the equilibrium. Furthermore, when employing an error-feedback control term to the slave neural network, parallel criteria regarding to the synchronization of the master neural network are also generated. Finally, some examples are given to illustrate the theoretical results.

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“…To improve system performance, various control strategies such as track control [15], adaptive control [16], feedback control [17], impulsive control [18] and intermittent control [19] are adopted based on the actual control requirements. Now, various stabilization criteria are also established such as exponential stabilization [20], mean square stabilization [21], guaranteed cost stabilization [22], finite-time stabilization [23,24], delay-independent stabilization [25], sampleddata stabilization [26]. As a whole, these stabilization strategies have been adopted in the light of different system structure analysis.…”

Section: Introductionmentioning

confidence: 99%

Periodically intermittent control strategies for $$\varvec{\alpha }$$ α -exponential stabilization of fractional-order complex-valued delayed neural networks

2018

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This paper is concerned with the global α-exponential stabilization for a class of fractionalorder complex-valued neural networks with time delay. To end this, some new fractionalorder differential inequalities are established, which improve and generalize previously known criteria. Then, a suitable periodically intermittent control scheme with time delay is proposed for the global α-exponential stabilization of the addressed networks, which include feedback control as a special case. By using the new fractional-order differential inequalities and coupling with the Lyapunov method and some other inequality techniques, some novel delay-independent criteria in terms of real-valued algebraic inequalities are obtained to ensure global α-exponential stabilization of the discussed networks, which are very simple to implement in practice and avoid complex computation on the matrix inequalities. Finally, an illustrative example with numerical simulations is given to demonstrate the effectiveness of the theoretical results.

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Globally exponential stabilization of neural networks with mixed time delays via impulsive control

Cited by 13 publications

References 47 publications

Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties

Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties

Stability of Inertial Neural Network with Time-Varying Delays Via Sampled-Data Control

Periodically intermittent control strategies for $$\varvec{\alpha }$$ α -exponential stabilization of fractional-order complex-valued delayed neural networks

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