A novel summation inequality for stability analysis of discrete-time neural networks

Liu, Xinge; Wang, Fengxian; Shu, Yanjun

doi:10.1016/j.cam.2016.03.006

Cited by 25 publications

(14 citation statements)

References 21 publications

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“…Therefore, the proposed method largely reduces the computational burden. In addition, we have modified the Lyapunov function by including the leakage terms

false(ie, - ϱ \sum_{i = k - ϱ}^{k - 1} μ^{T} false(i false) Z_{1} μ false(i false)

and

- ρ \sum_{j = k - ρ}^{k - 1} ν^{T} false(j false) Z_{2} ν false(j false)

) and proved that it is less conserved than the stability conditions obtained in the work of Liu et al (see Corollary ).…”

Section: Asymptotic Stability Resultsmentioning

confidence: 98%

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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“…Therefore, the proposed method largely reduces the computational burden. In addition, we have modified the Lyapunov function by including the leakage terms

false(ie, - ϱ \sum_{i = k - ϱ}^{k - 1} μ^{T} false(i false) Z_{1} μ false(i false)

and

- ρ \sum_{j = k - ρ}^{k - 1} ν^{T} false(j false) Z_{2} ν false(j false)

) and proved that it is less conserved than the stability conditions obtained in the work of Liu et al (see Corollary ).…”

Section: Asymptotic Stability Resultsmentioning

confidence: 98%

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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show abstract

“…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: 98%

“…Since most systems use a digital processor to acquire information from computers at discrete instants of time, it is essential to formulate discrete-time neural networks (DNNs) that are an analogue of continuous ones [11][12][13][14][15][16][17][18]. In order to improve results regarding this problem, various techniques have been applied to the delay-dependent category, such as augmented Lyapunov-Krasovskii (LK) functional [13,[19][20][21][22], free-weighting matrix method [18,23], summation inequality method [16,[24][25][26][27], delay-partitioning method [5,28,29] and reciprocally convex approach [20,30,31].…”

Section: Introductionmentioning

confidence: 99%

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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“…The authors in [25] proposed the concept of novel summation inequalities with time-varying delays to check the stability of neural networks. The results on Wirtinger based inequality has been proved by authors [26,27]. Liu in [28,29] investigated the impact of stability in exponential sense for discrete time BAM neural networks with some novel criterions and in [30] authors proposed discrete-time BAM neural networks in the sense of exponential.…”

Section: Introductionmentioning

confidence: 99%

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

Sowmiya¹,

Raja

Cao

et al. 2019

Asian Journal of Control

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This proposed research work aims to investigate the problem of uncertain BAM neural networks with leakage and discrete time‐varying delays in the sense of asymptotic stable by applying convex combination approach, discrete‐time Wirtinger inequality. It is pointed out that a novel summation inequality is entrenched based on discrete type Wirtinger based inequality. By the aid of novel inequality, reciprocally convex combination technique, time‐varying delays are examined to certify the stability of neural networks. Here, the uncertainties are considered as a randomly occurring parameter uncertainties and it conforms certain mutually uncorrelated Bernoulli‐distributed white noise sequences. The important feature of the results reported here is that the probability of occurrence of the parameter uncertainties are known a priori. To demonstrate the theoretical results of this research paper, numerical examples are given to expo the validity and efficiency of our results with the help of LMI Control toolbox in matlab.

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A novel summation inequality for stability analysis of discrete-time neural networks

Cited by 25 publications

References 21 publications

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

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

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

A delay‐dependent asymptotic stability criteria for uncertain BAM neural networks with leakage and discrete time‐varying delays: A novel summation inequality

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