Improved delay-dependent stability analysis of discrete-time neural networks with time-varying delay

Jiang, Lin; He, Yong; Wu, Min

doi:10.1016/j.jfranklin.2016.12.027

Cited by 42 publications

(19 citation statements)

References 31 publications

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“…Lemma 5. ( [57]) For a positive definite symmetric matrix R matrices  and  , the following statements are equivalent…”

Section:  mentioning

confidence: 99%

“…which was used to check the feasible region of stability criteria in [24,31,56,57,58]. The activation function is in the form of are computed with different lover bounds 1 h and the obtained results are given in Tab.…”

Section: Demonstrative Examplesmentioning

confidence: 99%

“…As a result of applying the mentioned techniques, some less conservative results are derived in [56]. As a result of applying the mentioned techniques, it is shown that the derived results are less conservative then the existing ones [24,31,57,58].…”

Section: Introductionmentioning

confidence: 97%

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Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

et al. 2021

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In this paper, we present the problem of stability, finite-time stability and passivity for discrete-time neural networks (DNNs) with variable delays. For the purposes of stability analysis, an augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two non-equidistant subintervals. Then, by using the Wirtinger-based inequality, reciprocally and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of LKF are given. In order to relax the existing results, several zero equalities are introduced and stability criteria are proposed in terms of linear matrix inequalities (LMIs). The main objective for the finite-time stability and passivity analysis is how to effectively evaluate the finite-time passivity conditions for DNNs. To achieve this, some weighted summation inequalities are proposed for application to a finite-sum term appearing in the forward difference of LKF, which helps to ensure that the considered delayed DNN is passive. The derived passivity criteria are presented in terms of linear matrix inequalities. Some numerical examples are presented to illustrate the proposed methodology.

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“…Lemma 5. ( [57]) For a positive definite symmetric matrix R matrices  and  , the following statements are equivalent…”

Section:  mentioning

confidence: 99%

Section: Demonstrative Examplesmentioning

confidence: 99%

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Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

et al. 2021

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“…Since the time delay signals in a dynamical system often leads to deterioration or instability of the system, the stability analysis of delayed NNs has important theoretical and practical significance. For instance, to the discrete-time neural networks with time-varying delay, authors in [24] proposed two improved delay-dependent stability rules by means of constructing a Lyapunov-Krasovskii functional with several augmented terms. In [25], based on the Lyapunov-Razumikhin techniques, the linear time-varying time-delay system could be ensured finite-time stability and finite-time contractive stability.…”

Section: Introductionmentioning

confidence: 99%

Finite-Time Stability and Stabilization of Impulsive Stochastic Delayed Neural Networks With Rous and Rons

et al. 2020

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This paper mainly tends to investigate finite-time stability and stabilization of impulsive stochastic delayed neural networks with randomly occurring uncertainties (ROUs) and randomly occurring nonlinearities (RONs). Firstly, by constructing the proper Lyapunov-Krasovskii functional and employing the average impulsive interval method, several novel criteria for ensuring the finite-time stability of impulsive stochastic delayed neural networks are obtained by means of linear matrix inequalities (LMIs). Then, some conditions about the state feedback controller are derived to ensure the finite-time stabilization of impulsive stochastic delayed neural networks with ROUs and RONs. Finally, numerical examples are provided to demonstrate the effectiveness and feasibility of the proposed results. INDEX TERMS Finite-time stability and stabilization, impulsive stochastic neural networks, average impulsive interval, time-varying delay, ROUs, RONs.

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“…With the help of some zero equalities and delay partitioning approach, the stability results have been proved in another work by Kwon et al Shu et al proposed the concept of stability issues by the aid of novel summation inequality. Jin et al delivered some stability conditions with the help of summation inequality and Wirtinger‐based inequality. Moreover, there are many results on the stability analysis of Markovian jumping NNs with time‐varying delays, eg, see other works .…”

Section: Introductionmentioning

confidence: 99%

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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Improved delay-dependent stability analysis of discrete-time neural networks with time-varying delay

Cited by 42 publications

References 31 publications

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

Stability, Finite-Time Stability and Passivity Criteria for Discrete-Time Delayed Neural Networks

Finite-Time Stability and Stabilization of Impulsive Stochastic Delayed Neural Networks With Rous and Rons

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

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