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Tu, Zhengwen; Jian, Jigui; Wang, Kang

Global exponential stability in Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions via LMI approach. (English) Zbl 1238.34141

Nonlinear Anal., Real World Appl. 12, No. 4, 2174-2182 (2011).
The global exponential stability in a Lagrange sense for recurrent neural networks with both time-varying delays and general activation functions is studied. Based on assuming that the activation functions are neither bounded nor monotonous or differentiable, several algebraic criteria in linear matrix inequality form for the global exponential stability in a Lagrange sense of neural networks are obtained by means of Lyapunov functions and Halanay delay differential inequality. Moreover, detailed estimations for a globally exponentially attractive set of recurrent neural networks with time-varying delays is established. When the system has a unique equilibrium point, the results obtained here show that the equilibrium point is globally exponentially stable in Lyapunov sense. Finally, two examples are given and analyzed to demonstrate our results.
Reviewer: Qintao Gan (Shijiazhuang)

Cited in 12 Documents

MSC:

34K20 Stability theory of functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics

Keywords:

neural network; Lagrange exponential stability; globally exponentially attractive set; Halanay delay differential inequality; LMI approach
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References:

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