A NEW CRITERION FOR STABILITY OF NEUTRAL-TYPE HOPFIELD NEURAL NETWORKS WITH CONSTANT DELAYS

Abstract

This paper makes some contributions to the stability problem of neutral-type Hopfield neural network model having a constant time delay in states of neurons and a constant neutral delay in the time derivatives of states of neurons. With the help of a suitable Lyapunov functional, a novel stability criterion is derived for neutral-type Hopfield neural network model. This stability criterion only requires to check the positive defineteness of the matrices involving the system elements of this type of neural networks. The presented stability condition proved to be independently of these time and neutral delays. Therefore, this condition can be easily justified by applying the properties of some certain matrices. A numerical example for this type of neutral systems is studied to show the applicability of the presented stability result. 

Keywords

• Neutral-Type Systems
• Hopfield Neural Networks
• Lyapunov Functionals
• Stability Analysis

Sabit Gecikmeler İçeren Nötral-Tip Hopfield Yapay Sinir Ağlarının Kararlılığı için Yeni Bir Kriter

Abstract

Bu makale, hem nöron durumlarının hem de nöron durumlarının türevlerinde sabit gecikmeler içeren nötral-tip Hopfield yapay sinir ağı modelinin kararlılık problemine yeni katkılar yapmaktadır. Uygun bir Lyapunov fonksiyoneli yardımıyla, nötral-tip Hopfield yapay sinir ağlarının kararlılığını sağlayan yeni bir kriter sunulmaktadır. Bu kararlılık kriterinin en önemli avantajı sadece sistem elemanlarından oluşan özel bir matrisin pozitif tanımlı olmasını test edilmesine dayandırılmış olmasıdır. Ayrıca, elde edilen kararlılık koşulu zaman ve nötral gecikmelerden bağımsızdır. Bu nedenle, elde edilen kararlılık kriterinin geçerliliği bazı özel matris özellikleri yardımıyla kolayca test edilebilir. Diğer yandan, önerilen kararlılık koşulunun uygulanabilirliğini göstermek amacıyla sayısal bir örnek verilmiştir.

Keywords

• Nötral-Tip Sistemler
• Hopfield Sinir Ağları
• Lyapunov Fonksiyonelleri
• Kararlılık Analizi

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