Global robust stability of delayed recurrent neural networks

Cao, Jinwei

doi:10.1016/s0960-0779(04)00236-x

Cited by 32 publications

(64 citation statements)

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“…However, as discussed in [3,4], in many electronic circuits, the input-output functions of amplifiers may be neither monotonically increasing nor continuously differentiable, hence nonmonotonic functions can be more appropriate to describe the neuron activation in designing and implementing an artificial neural network. In this paper, we make following assumption for the neuron activation functions, where the activation functions no longer need to be differentiable, monotonically increasing and bounded.…”

Section: Problem Formulationmentioning

confidence: 99%

“…[1,12,18]). In recent years, a great number of papers have been published on various neural networks with time delays, and the existence of equilibrium point, global asymptotic stability, global exponential stability, and the existence of periodic solutions have been intensively investigated, see [3,4,10,[15][16][17][19][20][21][22][23][24] for some recent results.…”

Section: Introductionmentioning

confidence: 99%

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Design of exponential state estimators for neural networks with mixed time delays

2007

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In this paper, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Design of exponential state estimators for neural networks with mixed time delays

2007

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“…Now, with the parameter ranges given by Equation (7), we have B 2 B 2 + B 2 [4]. Therefore, Equation (46) …”

Section: L N ) Owing To Equation (37) the Second Term In Eqmentioning

confidence: 99%

Global robust stability of interval delayed neural networks: Modified approach

Singh

2008

Circuit Theory & Apps

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SUMMARYA criterion for the global robust stability of Hopfield-type delayed neural networks with the intervalized network parameters is presented. The criterion, which is derived by utilizing the idea of splitting the given interval into two intervals, is in the form of linear matrix inequality and, hence, computationally tractable. The criterion yields a less conservative condition compared with many recently reported criteria, as is demonstrated with an example.

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“…Note that various classes of neural networks such as Hopfield neural networks [17,18], recurrent neural networks [19,20], cellular neural networks [21], Cohen-Grossberg neural networks [22], and bidirectional associative memory (BAM) neural networks [23][24][25] have been widely used in solving some signal processing, optimization, and image processing problems. In the last few years, some researchers have introduced fractional operators to neural networks to form fractional-order neural models [26][27][28][29][30], which could better describe the dynamical behaviors of the neurons.…”

Section: Introductionmentioning

confidence: 99%

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Zhang

Cao

et al. 2017

Complexity

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This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractionalorder hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the -layer and -layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.

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Global robust stability of delayed recurrent neural networks

Cited by 32 publications

References 0 publications

Design of exponential state estimators for neural networks with mixed time delays

Design of exponential state estimators for neural networks with mixed time delays

Global robust stability of interval delayed neural networks: Modified approach

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

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