Dissipativity analysis of neural networks with time-varying delays

Sun, Yan; Cui, Baotong

doi:10.1007/s11633-008-0290-x

Cited by 19 publications

(17 citation statements)

References 19 publications

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“…In , either Jensen's inequality or free weighting matrices approach are introduced to deal with integral terms. For instance, in , the authors considered the dissipativity and passivity problem of neural networks by constructing an LKF with double integral terms, which is reduced under Jensen's inequality. But in our paper, the LKF is constructed by using multiple integrals up to quadruple such as

\int_{t - τ}^{t} [η_{1}^{T} (t, s) U η_{1} (t, s) + (τ - t + s) η_{2}^{T} (s) V η_{2} (s) + {(τ - t + s)}^{2} {\overset{x}{true}}^{T} (s) W_{1} \overset{x}{true} (s) + {(τ - t + s)}^{3} {\overset{x}{true}}^{T} (s) W_{2} \overset{x}{true} (s)] normald s

along with the integral term

\int_{t - τ (t)}^{t} η_{1}^{T} (t, s) T η_{1} (t, s) normald s

.…”

Section: Resultsmentioning

confidence: 99%

Section: Remark 36mentioning

confidence: 99%

“…There are some remarkable features in Lemma 2.1, which can be highlighted by comparing with some existing results [17,18,26,27]. In [17,18,26,27], either Jensen's inequality or free weighting matrices approach are introduced to deal with integral terms. For instance, in [17,18,26,27], the authors considered the dissipativity and passivity problem of neural networks by constructing an LKF with double integral terms, which is reduced under Jensen's inequality.…”

Section: Remark 36mentioning

confidence: 99%

See 2 more Smart Citations

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

Nagamani

Radhika

2016

Math Methods in App Sciences

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In this paper, the robust dissipativity and passivity criteria for Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with time-varying delays have been investigated. The delay is of the time-varying nature, and the activation functions are assumed to be neither differentiable nor strictly monotonic. Furthermore, the description of the activation functions is more general than the commonly used Lipschitz conditions. By using a Lyapunov-Krasovskii functional and employing the quadratic convex combination approach, a set of sufficient conditions are established to ensure the dissipativity of the proposed model. The obtained conditions are presented in terms of linear matrix inequalities, so that its feasibility can be checked easily via standard numerical toolboxes. The quadratic convex combination approach used in our paper gives a reduced conservatism without using Jensen's inequality. In addition to that, numerical examples with simulation results are given to show the effectiveness of the obtained linear matrix inequality conditions.

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\int_{t - τ}^{t} [η_{1}^{T} (t, s) U η_{1} (t, s) + (τ - t + s) η_{2}^{T} (s) V η_{2} (s) + {(τ - t + s)}^{2} {\overset{x}{true}}^{T} (s) W_{1} \overset{x}{true} (s) + {(τ - t + s)}^{3} {\overset{x}{true}}^{T} (s) W_{2} \overset{x}{true} (s)] normald s

along with the integral term

\int_{t - τ (t)}^{t} η_{1}^{T} (t, s) T η_{1} (t, s) normald s

.…”

Section: Resultsmentioning

confidence: 99%

Section: Remark 36mentioning

confidence: 99%

Section: Remark 36mentioning

confidence: 99%

See 1 more Smart Citation

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

Nagamani

Radhika

2016

Math Methods in App Sciences

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“…Definition 2.1 [34] Given a scalar γ > 0, real symmetric matrices Q, R, and matrix S, the T-S fuzzy neural networks in (5) is called strictly (Q, R, S)-γ -dissipative, if for any t p ≥ 0, with zero initial condition, the following condition is satisfied:…”

Section: Lemma 23 [26]mentioning

confidence: 99%

Dissipativity and passivity analysis of T–S fuzzy neural networks with probabilistic time-varying delays: a quadratic convex combination approach

Nagamani

Radhika

2015

Nonlinear Dyn

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This paper studied dissipativity and passivity analysis of T-S fuzzy neural networks with distributed and probabilistic time-varying delay via quadratic convex combination approach. By introducing a stochastic variable with the Bernoulli distribution, the fuzzy neural networks with random time delays are transformed into one with deterministic delays and stochastic parameters. Moreover, it is well known that the dissipativity behavior of fuzzy neural networks is very sensitive to the time delay in the leakage term. By constructing proper Lyapunov-Krasovskii functional, new delay-dependent dissipativity and passivity conditions are derived in terms of linear matrix inequalities. Different from previous results, involving the first-order convex combination property, our derivation applies the idea of second-order convex combination and the property of quadratic convex function. Finally, numerical examples are provided to verify the effectiveness of the presented results.

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“…Considering the fact that time delays in the signal transmission between neurons can cause the oscillatory or even unstable phenomena [4][5][6]20,22,23,29,30], the stability analysis problem for delayed BAM neural networks has received much research interests. Sufficient conditions, either delay-dependent or delay-independent, have been proposed to guarantee the asymptotic or exponential stability for the BAM neural networks, see e.g.…”

mentioning

confidence: 99%

On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching

Liu

Wang

Liu

2009

Neural Process Lett

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In this paper, the stability analysis problem is investigated for stochastic bi-directional associative memory (BAM) neural networks with Markovian jumping parameters and mixed time delays. Both the global asymptotic stability and global exponential stability are dealt with. The mixed time delays consist of both the discrete delays and the distributed delays. Without assuming the symmetry of synaptic connection weights and the monotonicity and differentiability of activation functions, we employ the LyapunovKrasovskii stability theory and the Itô differential rule to establish sufficient conditions for the delayed BAM networks to be stochastically globally exponentially stable and stochastically globally asymptotically stable, respectively. These conditions are expressed in terms of the feasibility to a set of linear matrix inequalities (LMIs). Therefore, the global stability of the delayed BAM with Markovian jumping parameters can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. A simple example is exploited to show the usefulness of the derived LMI-based stability conditions.

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Dissipativity analysis of neural networks with time-varying delays

Cited by 19 publications

References 19 publications

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

A quadratic convex combination approach on robust dissipativity and passivity analysis for Takagi–Sugeno fuzzy Cohen–Grossberg neural networks with time‐varying delays

Dissipativity and passivity analysis of T–S fuzzy neural networks with probabilistic time-varying delays: a quadratic convex combination approach

On Global Stability of Delayed BAM Stochastic Neural Networks with Markovian Switching

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