<p>The analysis of globally asymptotic synchronization (GASN) for a kind of master–slave fractional-order fuzzy neural networks ( MSFOFNNS) is addressed in this discussion. Without utilizing linear matrix inequality (LMI), matrix measure theory (MMTY), and fractional inequalities, by L’Hopital’s rule of limit algorithms together with integral inequality method (IIMD), by constructing new controllers of time variable, two criteria assuring the GASN for the MSFOFNNS are established. So far, the synchronization in the case when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1899_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">$ \eta \in (0, 1)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> has been deeply investigated for master response fractional-order neural networks (MSFONNS). However, the synchronization in the case when <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1899_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$ \eta >1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> has rarely been discussed. In our study, the case when <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1899_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="72" /> </InlineMediaObject> <EquationSource Format="TEX">$ 0<\eta <1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo><</mo> <mi>η</mi> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> and the case when <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40435_2025_1899_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$ \eta >1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>η</mi> <mo>></mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, both are deeply discussed for the MSFOFNNS.</p>

Novel asymptotic synchronization conditions for fractional-order fuzzy neural networks

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发表日期：

2025年10月19日

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Yiping Shuai,
Zhengqiu Zhang

摘要

The analysis of globally asymptotic synchronization (GASN) for a kind of master–slave fractional-order fuzzy neural networks ( MSFOFNNS) is addressed in this discussion. Without utilizing linear matrix inequality (LMI), matrix measure theory (MMTY), and fractional inequalities, by L’Hopital’s rule of limit algorithms together with integral inequality method (IIMD), by constructing new controllers of time variable, two criteria assuring the GASN for the MSFOFNNS are established. So far, the synchronization in the case when $ \eta \in (0, 1)$ $η \in (0, 1)$ has been deeply investigated for master response fractional-order neural networks (MSFONNS). However, the synchronization in the case when $ \eta >1$ $η > 1$ has rarely been discussed. In our study, the case when $ 0<\eta <1$ $0 < η < 1$ and the case when $ \eta >1$ $η > 1$ , both are deeply discussed for the MSFOFNNS.