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Zbl 1166.93368
Qiu, Jianlong; Cao, Jinde
Delay-dependent exponential stability for a class of neural networks with time delays and reaction-diffusion terms. (English)
[J] J. Franklin Inst. 346, No. 4, 301-314 (2009). ISSN 0016-0032; ISSN 1879-2693/e

Summary: The exponential stability of a class of delayed neural networks described by nonlinear delay differential equations of the neutral type has been studied. By constructing appropriate Lyapunov functional and using the Linear Matrix Inequality (LMI) optimization approach, a series of sufficient criteria is obtained ensuring the existence, uniqueness and global exponential stability of an equilibrium point of such a kind of delayed neural networks. These conditions are dependent on the size of the time delay and the measure of the space, which is usually less conservative than delay-independent and space-independent ones. And, these networks are generalized without assuming the boundedness and differentiability of the activate functions. The proposed LMI condition can be checked easily by recently developed algorithms. The results are new and improve the earlier work. Examples are provided to demonstrate the effectiveness and applicability of the proposed criteria.

MSC 2000:: *93D20 Asymptotic stability of control systems
92B20 General theory of neural networks
93C20 Control systems governed by PDE

Keywords: neural networks; reaction-diffusion; delay; neutral type; exponential stability; linear matrix inequality

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Zentralblatt MATH Berlin [Germany]