Dissipativity Analysis for Stochastic Memristive Neural Networks With Time-Varying Delays: A Discrete-Time Case

Ding, Sanbo; Wang, Zhanshan; Zhang, Huaguang

doi:10.1109/tnnls.2016.2631624

Cited by 59 publications

(27 citation statements)

References 52 publications

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“…Denote

σ false(k false) = p \in scriptI

. To tackle the switched weights, we write system as a tractable framework based on logical switched functions as developed in the work of Ding et al, which can fully consider the excitatory and inhibitory effects of connection weights. Based on the switching property of DSMNNs (a), and an array of state‐dependent logical switched functions is defined by

δ_{i j}^{p} (x_{i} (k)) = \{\begin{matrix} sign ((), ŵ_{i j}^{p} - {\overset{w}{true}}_{i j}^{p}), & false| x_{i} false(k false) false| \leq π_{i}^{p}, \\ - sign ((), ŵ_{i j}^{p} - {\overset{w}{true}}_{i j}^{p}), & false| x_{i} false(k false) false| > π_{i}^{p} . \end{matrix}

Then, the DSMNNs (a) can be expressed as

x (k + 1) = {scriptA}_{p} x (k) + [W_{p} + E_{p} δ_{p} false(x false(k false) false) {\overset{E}{true}}_{p}] f (x (k)) + {scriptB}_{1, p} sat (u (k)) + {scriptB}_{2, p} ω (k),

where

\begin{matrix} alignleft \\ align-1 {scriptE}_{p} & = \end{matrix}

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

“…Memristive neural networks (MNNs) have attracted considerable attention since the memristor was firstly proposed by Chua in 1971, which were mainly motivated by their evident advantages such as lower energy consumption, stronger learning and memory ability, and lager storage capacity. Over the past years, the stability criteria, performance analysis, state estimation errors, and control problems for MNNs have been explored in depth, and some nice results have been yielded . Actually, in many real‐world applications, discrete‐time MNNs (DMNNs) are more applicable to image processing, pattern recognition, and computer simulation.…”

Section: Introductionmentioning

confidence: 99%

“…To a certain extent, the structure, properties, and dynamics of DMNNs have been changed greatly. However, there are few works on analyzing dynamical behaviors of DMNNs . Inspired by its applications, the study on the DMNNs is carried out in this paper.…”

Section: Introductionmentioning

confidence: 99%

“…Over the past years, the stability criteria, performance analysis, state estimation errors, and control problems for MNNs have been explored in depth, and some nice results have been yielded. [2][3][4][5][6][7][8][9][10][11][12] Actually, in many real-world applications, discrete-time MNNs (DMNNs) are more applicable to image processing, pattern recognition, and computer simulation. To a certain extent, the structure, properties, and dynamics of DMNNs have been changed greatly.…”

mentioning

confidence: 99%

“…In addition, dissipativity theory has become one of the main approaches to tackle the nonlinear systems with external disturbance. 10,35,36 As a special types of dissipativity, l 2 − l ∞ performance and passivity are also further developed nowadays. [37][38][39][40][41] So far, there is a little work that completely covers the exponential dissipativity and l 2 − l ∞ performance of DSMNNs.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

Wang

Jiang

et al. 2018

Intl J Robust & Nonlinear

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Summary The dissipativity of discrete‐time switched memristive neural networks with actuator saturation is considered in this paper. By constructing a quasi‐time‐dependent Lyapunov function, sufficient conditions are obtained to guarantee the exponential stability and exponential dissipativity for the closed‐loop system with mode‐dependent average dwell time switching. Furthermore, the exponential H∞ performance of discrete‐time switched memristive neural networks is also analyzed, while the quasi‐time‐dependent controller and observer gains of the desired exponential dissipative and H∞ performance can be calculated from linear matrix inequalities. Finally, the effectiveness of theoretical results is illustrated through the numerical examples.

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“…Denote

σ false(k false) = p \in scriptI

δ_{i j}^{p} (x_{i} (k)) = \{\begin{matrix} sign ((), ŵ_{i j}^{p} - {\overset{w}{true}}_{i j}^{p}), & false| x_{i} false(k false) false| \leq π_{i}^{p}, \\ - sign ((), ŵ_{i j}^{p} - {\overset{w}{true}}_{i j}^{p}), & false| x_{i} false(k false) false| > π_{i}^{p} . \end{matrix}

Then, the DSMNNs (a) can be expressed as

x (k + 1) = {scriptA}_{p} x (k) + [W_{p} + E_{p} δ_{p} false(x false(k false) false) {\overset{E}{true}}_{p}] f (x (k)) + {scriptB}_{1, p} sat (u (k)) + {scriptB}_{2, p} ω (k),

where

\begin{matrix} alignleft \\ align-1 {scriptE}_{p} & = \end{matrix}

…”

Section: Problem Formulation and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

Wang

Jiang

et al. 2018

Intl J Robust & Nonlinear

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show abstract

Enhanced result on stability analysis of randomly occurring uncertain parameters, leakage, and impulsive BAM neural networks with time‐varying delays: Discrete‐time case

Sowmiya

Raja

Cao

et al. 2018

Adaptive Control & Signal

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In real-world problems, neural networks play an increasingly important role in terms of both theory and applications. In this paper, the asymptotic stability analysis issue is investigated for uncertain impulsive discrete-time bidirectional associative memory neural networks with leakage and time-varying delays. With the assistance of novel summation inequality, reciprocally convex combination technique, and triple Lyapunov-Krasovskii functionals terms, many cases of time-varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainty, and it conforms certain mutually uncorrelated Bernoulli-distributed white noise sequences. An important feature of the results reported here is that the probability of occurrence of the parameter uncertainties specify a priori estimate. Finally, numerical examples are proposed to expose the capability and efficiency of our research work with the help of the LMI control toolbox in MATLAB.

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Dissipativity and synchronization control of fractional‐order memristive neural networks with reaction‐diffusion terms

Gao

2019

Math Methods in App Sciences

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This paper deals with the dissipativity and synchronization control of fractional-order memristive neural networks (FOMNNs) with reaction-diffusion terms. By means of fractional Halanay inequality, Wirtinger inequality, and Lyapunov functional, some sufficient conditions are provided to ensure global dissipativity and exponential synchronization of FOMNNs with reaction-diffusion terms, respectively. The underlying model and the obtained results are more general since the reaction-diffusion terms are first introduced into FOMNNs. The given conditions are easy to be checked, and the correctness of the obtained results is confirmed by a living example. KEYWORDS fractional-order, memristive neural network, reaction-diffusion term MSC CLASSIFICATION 34H05; 34D06; 34K37 INTRODUCTIONChua 1 first proposed the concept of memristor to describe the relationship between magnetic flux and charge, yet its actual implementation was made by HP team in 2008 with doped titanium dioxide. 2 Since then, memristor has attracted world-class attention due to its potential application in the next generation of human brain-like computers, and many excellent researches have emerged. 3-6 Wu and Zeng 3 provide an exponential stabilization condition of memristive neural networks (MNNs) in terms of linear matrix inequalities (LMIs), and Yang et al 4 study exponential synchronization of MNNs with heterogeneous delays by using interval matrix method to deal with memristive coefficients. A less conservative criterion for synchronization of MNNs is obtained in Zhang et al 5 by introducing an adjustable parameter into a discontinuous controller. For delayed MNNs, Wang and Shen 6 develop some algebraic criteria for the finite-time stabilizability by using M-matrix and also establishes the instabilizability conditions. It is worth mentioning that the above models are only first-order dynamical systems and do not involve fractional-order ones.Differing from integer-order derivative, fractional-order derivative can better depict some nonclassical phenomena in natural science and engineering applications. 7 Then, it has potential applications in signal processing, electromagnetism, quantum evolution of complex systems, and so on. 8 As a result, fractional-order neural network (FONN) has entered the public field of vision, and some entertaining works have been published. 7-13 For instance, the stability of the equilibrium point for complex-valued delayed FOMNNs is analyzed in Wei et al 7 by nonlinear measure method and contraction mapping theory, and the adaptive synchronization control of FOMNNs with time delay is discussed in Bao et al 9 via a fractional-order inequality. The Mittag-Leffler stabilization condition for a class of FOMNNs is established in Wu and Math Meth Appl Sci. 2019;42:7494-7505. wileyonlinelibrary.com/journal/mma

show abstract

Dissipativity Analysis for Stochastic Memristive Neural Networks With Time-Varying Delays: A Discrete-Time Case

Cited by 59 publications

References 52 publications

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

Enhanced result on stability analysis of randomly occurring uncertain parameters, leakage, and impulsive BAM neural networks with time‐varying delays: Discrete‐time case

Dissipativity and synchronization control of fractional‐order memristive neural networks with reaction‐diffusion terms

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