Corrigendum to “Delay-dependent stability for uncertain stochastic neural networks with time-varying delay” [Physica A 381 (2007) 93–103]
Corrigendum to “Delay-dependent stability for uncertain stochastic neural networks with time-varying delay” [Physica A 381 (2007) 93–103]
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DOI：
10.1016/j.physa.2007.10.016
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发表时间：
2008-02
影响因子：
3.3
通讯作者：
He Huang;G. Feng
中科院分区：
文献类型：
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作者：
He Huang;G. Feng
在参考文献1中的示例1中存在数值计算错误。[1]的文件。实际上，最大允许时间延迟为τ max= 0.0664，可行解如下：P=[86.7630 34.8178 45.9634 34.8178 23.2443 26.9313 45.9634 26.9313 93.1159]，R=[68.4118 9.6563 14.3037 9.6563 5.9102− 0.2315 14.3037− 0.2315 28.4168]，S=[335.8701 59.5085 67.9444 59.5085 53.6136 - 4.8795 67.9444 - 4.8795 126.5213]，E=[113.3260 28.0701 23.5101 80.8653 0.2022 5.1510 108.8390 16.8910 6.4998]，F=[63.0862 10.3004− 22.9350 7.6376 21.0553− 4.2358 23.9666 3.1873 34.0715]，α= 148.4591，β= 69.9375，γ= 120.7774。[1]的文件。考虑具有以下参数的神经网络：A=[4 0 0 5]，W 0=[0.4− 0.7 0.1 0]，W 1=[− 0.2 0.6 0.5− 0.1]，C=[0.5 0 0 0.5]，D=[0− 0.5− 0.5 0]，M=[0.1− 0.1] T，N 1=[0.2 0.3]，N 2=[0.2− 0.3]，N 3=[− 0.2− 0.3]，L= 0.5 I。通过Matlab LMI控制器求解定理2中的LMI条件，最大允许时延τ max= 0.4109，得到可行解P=[92.9271 - 51.2610 - 51.2610 93.7349]，R=[57.0420 - 23.8028 - 23.8028 53.8782]，S=[164.3363− 20.0979− 20.0979 167.2846]，E=[38.1468− 71.0418− 72.3039 38.3007]，F=[42.3643− 6.2409− 6.1531 41.6031]，α= 81.9504，β= 21.3014，γ= 45.7762.这意味着对于τ∈[0，0.4109]，神经网络在均方上是全局渐近稳定的。
There was a numerical computation error in Example 1 in Ref.[1]. In fact, the maximum allowed time delay is τ max= 0.0664 with the following feasible solution: P=[86.7630 34.8178 45.9634 34.8178 23.2443 26.9313 45.9634 26.9313 93.1159], R=[68.4118 9.6563 14.3037 9.6563 5.9102− 0.2315 14.3037− 0.2315 28.4168], S=[335.8701 59.5085 67.9444 59.5085 53.6136− 4.8795 67.9444− 4.8795 126.5213], E=[113.3260 28.0701 23.5101 80.8653 0.2022 5.1510 108.8390 16.8910 6.4998], F=[63.0862 10.3004− 22.9350 7.6376 21.0553− 4.2358 23.9666 3.1873 34.0715], α= 148.4591, β= 69.9375, γ= 120.7774.Here, we give another example to demonstrate the application of Theorem 2 in Ref.[1]. Consider a neural network with the following parameters A=[4 0 0 5], W 0=[0.4− 0.7 0.1 0], W 1=[− 0.2 0.6 0.5− 0.1], C=[0.5 0 0 0.5], D=[0− 0.5− 0.5 0], M=[0.1− 0.1] T, N 1=[0.2 0.3], N 2=[0.2− 0.3], N 3=[− 0.2− 0.3], L= 0.5 I. By solving the LMI condition in Theorem 2 via Matlab LMI Control Toolbox, the maximum allowed time delay is τ max= 0.4109 and a feasible solution is obtained as P=[92.9271− 51.2610− 51.2610 93.7349], R=[57.0420− 23.8028− 23.8028 53.8782], S=[164.3363− 20.0979− 20.0979 167.2846], E=[38.1468− 71.0418− 72.3039 38.3007], F=[42.3643− 6.2409− 6.1531 41.6031], α= 81.9504, β= 21.3014, γ= 45.7762. It means that for τ∈[0, 0.4109], the neural network is globally asymptotically stable in the mean square.