## Abstract and Applied Analysis

### Global μ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays

#### Abstract

The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the global $\mu$-stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 397532, 14 pages.

Dates
First available in Project Euclid: 27 February 2015

https://projecteuclid.org/euclid.aaa/1425048768

Digital Object Identifier
doi:10.1155/2014/397532

Mathematical Reviews number (MathSciNet)
MR3216046

#### Citation

Chen, Xiaofeng; Song, Qiankun; Liu, Yurong; Zhao, Zhenjiang. Global μ -Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 397532, 14 pages. doi:10.1155/2014/397532. https://projecteuclid.org/euclid.aaa/1425048768

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