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Global Asymptotic Stability for Complex-Valued Neural Networks with Time-Varying Delays via New Lyapunov Functionals and Complex-Valued Inequalities

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Abstract

By constructing novel Lyapunov functionals and using some new complex-valued inequalities, a new LMI-based sufficient condition on global asymptotic stability of equilibrium point for complex-valued recurrent neural networks with time-varying delays is established. In our result, the assumption for boundedness in existing papers on the complex-valued activation functions is removed and the matrix inequalities used in recent papers are replaced with new matrix inequalities. On the other hand, we construct new Lyapunov functionals which are different from those constructed in existing papers. Hence, our result is less conservative, new and complementary to the previous results.

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Acknowledgements

Funding was provided by Education Department of Hunan Province (Grant No. 201485).

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Zhengqiu Zhang & Dangli Hao

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  1. Zhengqiu Zhang
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  2. Dangli Hao
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Correspondence to Zhengqiu Zhang.

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Zhang, Z., Hao, D. Global Asymptotic Stability for Complex-Valued Neural Networks with Time-Varying Delays via New Lyapunov Functionals and Complex-Valued Inequalities. Neural Process Lett 48, 995–1017 (2018). https://doi.org/10.1007/s11063-017-9757-5

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