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

Liu, Yurong; Wang, Zidong; Liu, Xiaohui

doi:10.1007/s11063-009-9107-3

Cited by 15 publications

(3 citation statements)

References 31 publications

(31 reference statements)

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“…For this, we construct the triple integral term

\int_{- σ_{1}}^{0} \int_{θ}^{0} \int_{t + γ}^{t} e^{γ_{0} (s - γ)} z_{1}^{T} (s) K_{5} z_{1} (s) d s d γ d θ

for eliminating the corresponding integral

\sum_{j = 1}^{N} δ_{i j} \int_{- σ_{1}}^{0} \int_{t + θ}^{t} e^{γ_{0} (s - θ)} z_{1}^{T} (s) M_{5 j} z_{1} (s) d s d θ

. This treatment is different from the ones in and may lead to obtain an improved feasible region for global stability criteria. Now, in this part, we concentrate on the stochastic BAM neural networks with Markovian switching and mode‐dependent probabilistic time‐varying delays, which is represented by

true{\begin{matrix} left & d x (t) & = & [- A (r (t)) x (t) + B_{1} (r (t)) f (y (t)) + α_{0} B_{2} (r (t)) f (y (t - τ_{1} (t, r (t)))) \\ left & + (1 - α_{0}) B_{2} (r ( \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

“…This treatment is different from the ones in [51,52] and may lead to obtain an improved feasible region for global stability criteria. Now, in this part, we concentrate on the stochastic BAM neural networks with Markovian switching and mode-dependent probabilistic time-varying delays, which is represented by Þ5r 1i t ð Þ; r 2 t; r t ð Þ ð Þ 5r 2i t ð Þ: It is assumed that there exist scalars s 1i > 0; s 2i > 0; r 1i > 0; r 2i > 0 and s l1i > 0; s l2i > 0; r l1i > 0; r l2i > 0 such that for each i51; 2; .…”

Section: Remark 31mentioning

confidence: 95%

See 1 more Smart Citation

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

et al. 2014

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In this article, an exponential stability analysis of Markovian jumping stochastic bidirectional associative memory (BAM) neural networks with mode‐dependent probabilistic time‐varying delays and impulsive control is investigated. By establishment of a stochastic variable with Bernoulli distribution, the information of probabilistic time‐varying delay is considered and transformed into one with deterministic time‐varying delay and stochastic parameters. By fully taking the inherent characteristic of such kind of stochastic BAM neural networks into account, a novel Lyapunov‐Krasovskii functional is constructed with as many as possible positive definite matrices which depends on the system mode and a triple‐integral term is introduced for deriving the delay‐dependent stability conditions. Furthermore, mode‐dependent mean square exponential stability criteria are derived by constructing a new Lyapunov‐Krasovskii functional with modes in the integral terms and using some stochastic analysis techniques. The criteria are formulated in terms of a set of linear matrix inequalities, which can be checked efficiently by use of some standard numerical packages. Finally, numerical examples and its simulations are given to demonstrate the usefulness and effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 39–65, 2015

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“…For this, we construct the triple integral term

\int_{- σ_{1}}^{0} \int_{θ}^{0} \int_{t + γ}^{t} e^{γ_{0} (s - γ)} z_{1}^{T} (s) K_{5} z_{1} (s) d s d γ d θ

for eliminating the corresponding integral

\sum_{j = 1}^{N} δ_{i j} \int_{- σ_{1}}^{0} \int_{t + θ}^{t} e^{γ_{0} (s - θ)} z_{1}^{T} (s) M_{5 j} z_{1} (s) d s d θ

true{\begin{matrix} left & d x (t) & = & [- A (r (t)) x (t) + B_{1} (r (t)) f (y (t)) + α_{0} B_{2} (r (t)) f (y (t - τ_{1} (t, r (t)))) \\ left & + (1 - α_{0}) B_{2} (r ( \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

Section: Remark 31mentioning

confidence: 95%

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

et al. 2014

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“…Agents in system were connected via a certain connection rule; two algebraic sufficient conditions were derived under the circumstance that the topology was uncontrollable. Reference [27] investigated the stability analysis problem on neural networks with Markovian jumping parameters. Both of Lyapunov-Krasovskii stability theory and Itô differential rule were established to deal with global asymptotic stability and global exponential stability.…”

Section: Introductionmentioning

confidence: 99%

Fault Detection for Wireless Networked Control Systems with Stochastic Switching Topology and Time Delay

Guo

Zhang

Karimi

et al. 2014

Abstract and Applied Analysis

Self Cite

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This paper deals with the fault detection problem for a class of discrete-time wireless networked control systems described by switching topology with uncertainties and disturbances. System states of each individual node are affected not only by its own measurements, but also by other nodes’ measurements according to a certain network topology. As the topology of system can be switched in a stochastic way, we aim to designH∞fault detection observers for nodes in the dynamic time-delay systems. By using the Lyapunov method and stochastic analysis techniques, sufficient conditions are acquired to guarantee the existence of the filters satisfying theH∞performance constraint, and observer gains are derived by solving linear matrix inequalities. Finally, an illustrated example is provided to verify the effectiveness of the theoretical results.

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Direct Delay Decomposition Approach to Robust Stability on Fuzzy Markov-Type BAM Neural Networks with Time-Varying Delays

Sathy

Balasubramaniam

2012

Mathematical Modelling and Scientific Computation

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

Cited by 15 publications

References 31 publications

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

Exponential stability for markovian jumping stochastic BAM neural networks with mode‐dependent probabilistic time‐varying delays and impulse control

Fault Detection for Wireless Networked Control Systems with Stochastic Switching Topology and Time Delay

Direct Delay Decomposition Approach to Robust Stability on Fuzzy Markov-Type BAM Neural Networks with Time-Varying Delays

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