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Zbl 1121.34078
Ren, Fengli; Cao, Jinde
LMI-based criteria for stability of high-order neural networks with time-varying delay.
(English)
[J] Nonlinear Anal., Real World Appl. 7, No. 5, 967-979 (2006). ISSN 1468-1218

The authors consider a class of high-order neural networks with time-varying delay of the form $$x^{\prime}_i(t) = -a_i x_i(t) +{\sum}_{j=1}^Lw_{ij}{\Pi}_{k\in I_j}[g_k(x_k(t))]^{d_k(j)} + {\sum}_{j=1}^Lw_{ij}^{\tau}{\Pi}_{k\in I_j}[g_k(x_k(t-\tau (t)))]^{d_k(j)}$$ for $i=1,2,\dots, n$. Under appropriate assumptions this system has a unique equilibrium point. Additional sufficient conditions for the global exponential stability of the equilibrium point are formulated. Some numerical examples are given to illustrate the theoretical results.
[Gheorghe Moroşanu (Budapest)]
MSC 2000:
*34K20 Stability theory of functional-differential equations
92B20 General theory of neural networks

Keywords: global exponential stability; Lyapunov functional

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