Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach

Liao, Xiaofeng; Chen, Guanrong; Sánchez, Edgar N.

doi:10.1016/j.neunet.2003.08.001

Cited by 78 publications

(118 citation statements)

References 4 publications

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“…It is well known that neural networks are highly complex and large-scale nonlinear dynamical systems [1,[25][26][27][28][29][30][31][32][33][34][35]. Lacking the ability to tackle the intrinsic complexities, neural network models under investigation today have been dramatically simplified [7, 9-16, 18-24, 36, 37, 39-42].…”

Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis in tri-neuron model with time delay

Liao

Guo

2007

Nonlinear Dyn

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A simple delayed neural network model with three neurons is considered. By constructing suitable Lyapunov functions, we obtain sufficient delaydependent criteria to ensure global asymptotical stability of the equilibrium of a tri-neuron network with single time delay. Local stability of the model is investigated by analyzing the associated characteristic equation. It is found that Hopf bifurcation occurs when the time delay varies and passes a sequence of critical values. The stability and direction of bifurcating periodic solution are determined by applying the normal form theory and the center manifold theorem. If the associated characteristic equation of linearized system evaluated at a critical point involves a repeated pair of pure imaginary eigenvalues, then the double Hopf bifurcation is also found to occur in this model. Our main attention will be paid to the double Hopf bifurcation associated with resonance. Some Numerical examples are finally given for justifying the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Stability and bifurcation analysis in tri-neuron model with time delay

Liao

Guo

2007

Nonlinear Dyn

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“…Delays in neural networks caused by neural processing and signal transmission may cause oscillation, divergence, and instability such that the performances of the networks are degraded [1,12,13]. Therefore, a large amount of results on stability analysis for neural networks with delays have been reported in the literature, for example [14][15][16][17][18][19][20][21][22][23][24][25][26][27], and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Passivity analysis of stochastic time-delay neural networks

et al. 2010

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Passivity analysis of stochastic neural networks with time-varying delays and parametric uncertainties is investigated in this paper. Passivity of stochastic neural networks is defined. Both delayindependent and delay-dependent stochastic passivity conditions are presented in terms of linear matrix inequalities (LMIs). The results are established by using the Lyapunov-Krasovskii functional method. In order to derive the delay-dependent passivity criterion, some free-weighting matrices are introduced. The effectiveness of the method is illustrated by numerical examples.

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“…As well known, many widely accepted principles for the robust controller design can be considered as a special case of LMI problems [1,2]. With the help of LMI, specific Lyapunov functions can be constructed to analyze the stability and performance of linear differential inclusions and delayed dynamical systems [3,4]. Several system identification problems and the inverse problems of optimal control employ the LMI approach as a powerful tool [5,6].…”

Section: Introductionmentioning

confidence: 99%

A Simplified Neural Network for Linear Matrix Inequality Problems

Cheng

Hou

Tan

2009

Neural Process Lett

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A simplified neural network model is proposed to solve a class of linear matrix inequality problems. The stability and solvability of the proposed neural network are analyzed and discussed theoretically. In comparison with the previous neural network models (Lin and Huang, Neural Process Lett 11:153-169, 2000; Lin et al., IEEE Trans Neural Netw 11:1078-1092, the simplified one is composed of two layers rather than three layers, and the neuron array in each layer is triangular rather than square. The proposed approach can therefore reduce the complexity of the neural network architecture. In addition, the simplified neural network can also be extended to solve multiple linear matrix inequalities with specific constraints, which enlarges the application domain of the proposed approach. Finally, examples are given to illustrate the effectiveness and efficiency of the simplified neural network.

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Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach

Cited by 78 publications

References 4 publications

Stability and bifurcation analysis in tri-neuron model with time delay

Stability and bifurcation analysis in tri-neuron model with time delay

Passivity analysis of stochastic time-delay neural networks

A Simplified Neural Network for Linear Matrix Inequality Problems

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