Robust Stability Analysis of Uncertain Neural Networks with Time-Varying Delay-A Linear Matrix Inequality Approach

時變時延不定隨機類神經網路之強健穩定度－線性矩陣不等式方法

劉柄麟(Pin-Lin Liu)

《建國科大學報》 27卷3期 (2008/04) Pp. 15-45

https://doi.org/10.6995/JCTU.200804.0015

摘要

本論文旨在探討區間時變時延不定參數隨機類神經網路系統之強健穩定度。應用奇異模型轉換技巧、特殊型Lyapunov-Krasovskii泛函數方法、相似型Leibniz-Newton公式、線性矩陣不等式觀念針對上述類神經網路系統，提出新穩定測試準則。本論文分為三個主要部份。第一部份針對具有常數參數之時延隨機Hopfield型類神經網路系統，提出時延相關之漸近穩定測試準則。第二部份針對具有參數擾動Cellular型類神經網路系統，提出時延相關的強健穩定測試準則。第三部份是關於具有不定參數之時變時延隨機類神經網路系統，提出強健穩定的充分條件。推導定理公式過程中，網路之激發函數不需滿足S型函數之假設。關於引用奇異模型轉換技巧之目的，可減少二次不等式項目。舉例證實本研究方法可避免求解矩陣方程式（包括Lyapunov方程式與Riccati方程式）之步驟且改善現有文獻之穩定條件。另外，本論文所提出之方法亦可用來分析具有不定參數之大型時變時延隨機類神經網路系統的穩定度問題當作另一可行之研究方向。

關鍵字

隨機類神經網路 ； 區間時變時延 ； 奇異模型轉換 ； 線性矩陣不等式

並列摘要

In this paper, we investigate the problem of robust stability for uncertain stochastic neural network systems with interval time-varying delay. By means of singular model transformation technique, special Lyapunov-Krasovskii functional approach, similar Leibniz-Newton formula and linear matrix inequality (LMI) concept, some new stability conditions are derived for above systems. There are three main parts concerning our research results. The first result is to propose both delay-independent and delay-dependent criteria for guaranteeing the asymptotic stability of stochastic switched Hopfield neural network systems with constant parameters and time delay. The second result is to present several new delay-dependent criteria for testing the mean-square exponential stability of stochastic cellular neural network systems with interval time-varying delay. The third result is to provide sufficient conditions for ensuring asymptotic stability of stochastic neural network systems with uncertain parameters and interval time-varying delay. In the results, we do not assume that the network's activation functions are with the property of sigmoid function. The purpose of introducing the singular model transformation is to improve the results on bounds of the inner product of two vectors. Our results do not need the solution of Lyapunov equation or Riccati equation. Compared with existing results in the literature, our method is shown to be superior to other ones. Numerical examples are given to demonstrate the effectiveness of the proposed approach. Besides, our approach can be also applied to the stability testing problem for large-scale stochastic neural network systems with uncertain parameters and time-varying delays.

並列關鍵字

Stochastic neural network ； interval time-varying delay ； singular model transformation ； linear matrix inequality