Non-fragile robust finite-time stabilization and $$H_{\infty }$$H∞ performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching

Peng, Xiao; Wu, Huaiqin

doi:10.1007/s00521-018-3682-z

Cited by 41 publications

(11 citation statements)

References 57 publications

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“…Calculating the infinitesimal generator of V 1 (e i (t), r, t) along the trajectory of system (19), yields…”

Section: Resultsmentioning

confidence: 99%

“…On the basis of Lemma 1, system (19) is the global fixed-time stable. This means that system (14) can achieve the global fixed-time synchronization, and the stochastic settling-time is bounded by…”

Section: Resultsmentioning

confidence: 99%

“…Synchronization, which is a fundamental phenomenon of dynamical behavior in network systems, has been extensively studied in the past few decades, thus, a large number of results on synchronization have been reported, such as exponential synchronization, adaptive synchronization, lag synchronization, fixed/finite-time synchronization, projective synchronization, complete synchronization, and cluster synchronization, dissipativity synchronization, H-infinity synchronization. [16][17][18][19][20][21][22][23][24][25][26] In Reference 16, the authors investigated the global exponential synchronization problem for CVDNs by exploiting delayed impulsive control under stochastic perturbations. In Reference 17, the authors considered the global finite-time synchronization for fractional-order discontinuous neural networks by the nonfragile control approach.…”

Section: Introductionmentioning

confidence: 99%

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Fixed‐time synchronization for discontinuous delayed complex‐valued networks with semi‐Markovian switching and hybrid couplings via adaptive control

Liu

Cao

2020

Adaptive Control & Signal

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In this article, the global fixed-time synchronization issue is considered for semi-Markovian switching discontinuous complex-valued dynamical networks (CVDNs) with hybrid couplings and time-varying delays, in which CVDNs are not divided into two real value systems, contrary to existing literature. First, a new fixed-time convergence principle for complex-valued nonlinear system with semi-Markovian switching is developed. Second, to realize the fixed-time synchronization, the state feedback controller with integral term and adaptive controller are designed, respectively. Under the complex-valued differential inclusions framework, by utilizing Lyapunov-Krasovskii functional method and inequality analysis technique, the global fixed-time synchronization conditions are addressed in terms of linear matrix inequalities. Finally, two numerical simulations are given to illustrate the validity of the presented theoretical results.

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“…Calculating the infinitesimal generator of V 1 (e i (t), r, t) along the trajectory of system (19), yields…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fixed‐time synchronization for discontinuous delayed complex‐valued networks with semi‐Markovian switching and hybrid couplings via adaptive control

Liu

Cao

2020

Adaptive Control & Signal

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“…[22,23,32,33] In fact, it is more desirable for networks to reach synchronization in a finite-time and achieve optimization in convergence time in physical and engineering. [34][35][36] Hence, it is necessary to investigate the finite-time synchronization of FMNN.…”

Section: Introductionmentioning

confidence: 99%

Finite-time Mittag–Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions*

Chen

Ding

et al. 2020

Chinese Phys. B

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The finite-time Mittag–Leffler synchronization is investigated for fractional-order delayed memristive neural networks (FDMNN) with parameters uncertainty and discontinuous activation functions. The relevant results are obtained under the framework of Filippov for such systems. Firstly, the novel feedback controller, which includes the discontinuous functions and time delays, is proposed to investigate such systems. Secondly, the conditions on finite-time Mittag–Leffler synchronization of FDMNN are established according to the properties of fractional-order calculus and inequality analysis technique. At the same time, the upper bound of the settling time for Mittag–Leffler synchronization is accurately estimated. In addition, by selecting the appropriate parameters of the designed controller and utilizing the comparison theorem for fractional-order systems, the global asymptotic synchronization is achieved as a corollary. Finally, a numerical example is given to indicate the correctness of the obtained conclusions.

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“…It is known to us all, time delays are often inevitable due to internal or external uncertainties in signal transmission. And the produced time delays may cause the stability of the system and even results in oscillation, divergence, and instability phenomena 27‐30 . Thus, much achievement has been devoted to analyze dynamic behaviors of MNNs with various types of time delays (see, eg, References 6 and 31‐35).…”

Section: Introductionmentioning

confidence: 99%

New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms

Cao

Xiong

et al. 2020

Intl J Robust & Nonlinear

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This article deals with the problems of exponential stability and extended dissipative analysis for a class of uncertain memristive neural networks (MNNs) with additive time-varying delays and reaction-diffusion terms. On the basis of generalized Lyapunov functional approach, Hardy-Poincarè inequality, Jensen's inequality, as well as some other inequality techniques, it is shown that the issues of exponential stability and extended dissipativity for the uncertain reaction-diffusion MNNs are solvable if a set of linear matrix inequalities (LMIs) proposed are feasible. As a special case, the conditions on exponential stability and extended dissipativity for the uncertain MNNs with additive time-varying delays are also obtained and given in terms of nonlinear matrix inequalities (NMIs). The obtained NMIs can be transformed as general LMIs via using a new quadratic convex combination skill. Moreover, the developed sufficient conditions for the uncertain delayed MNNs with and without reaction-diffusion terms can be easily checked by Matlab LMI control toolbox, and three numerical examples with simulation are provided to show the effectiveness and applicability of the theoretical results.

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Non-fragile robust finite-time stabilization and $$H_{\infty }$$H∞ performance analysis for fractional-order delayed neural networks with discontinuous activations under the asynchronous switching

Cited by 41 publications

References 57 publications

Fixed‐time synchronization for discontinuous delayed complex‐valued networks with semi‐Markovian switching and hybrid couplings via adaptive control

Fixed‐time synchronization for discontinuous delayed complex‐valued networks with semi‐Markovian switching and hybrid couplings via adaptive control

Finite-time Mittag–Leffler synchronization of fractional-order delayed memristive neural networks with parameters uncertainty and discontinuous activation functions*

New results on stability analysis and extended dissipative conditions for uncertain memristive neural networks with two additive time‐varying delay components and reaction‐diffusion terms

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