Comments on “Absolute exponential stability of a class of neural networks with unbounded delay”

✍ Scribed by Da-Wei Chang

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 137 KB
• Volume: 20
• Category: Article
• ISSN: 0893-6080
• DOI: 10.1016/j.neunet.2007.01.005

✦ Synopsis

Recently, Zhang, Suda and Iwasa [Zhang, Jiye, Suda, Yoshihiro, & Iwasa, Takashi (2004). Absolute exponential stability of a class of neural networks with unbounded delay, Neural Network, 17, 391-397] established the following:

Result. Suppose that T be an n × n matrix, and D be an n × n positive definite diagonal matrix. For each n × n diagonal matrix K ≥ 0, we have det(-T K + D) > 0, if and only if, -T ∈ P 0 (cf. Lemma 2 given by Zhang, Suda, and Iwasa ( 2004)).

In this letter, we would like to point out that the necessary condition in above Result given by Zhang et al. ( 2004) is incorrect in general.