Global Stability Criterion for Delayed Complex-Valued Recurrent Neural Networks

• Published in: IEEE transaction on neural networks and learning systems Vol. 25; no. 9; pp. 1704 - 1708
• Main Authors: Zhang, Ziye, Lin, Chong, Chen, Bing
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.09.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Artificial intelligence; Asymptotic properties; Asymptotic stability; Complex-valued neural networks; Criteria; Equivalence; global stability; Learning; Neural networks; Numerical stability; Recurrent neural networks; Stability; Stability criteria; time delay; Uniqueness; global stability; Complex-valued neural networks; time delay
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2013.2288943

The stability problem for delayed complex-valued recurrent neural networks is considered in this paper. By separating complex-valued neural networks into real and imaginary parts, forming an equivalent real-valued system, and constructing appropriate Lyapunov functional, a sufficient condition to ascertain the existence, uniqueness, and globally asymptotical stability of the equilibrium point of complex-valued systems is provided in terms of linear matrix inequality. Meanwhile, the errors in the recent work are pointed out, and even if the result therein is correct, it is shown that our result not only improves but also generalizes in that work. Numerical examples are given to show the effectiveness and merits of the present result.