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基于LMI方法的時滯BAM神經(jīng)網(wǎng)絡(luò)的全局穩(wěn)定性分析

劉妹琴,  顏鋼鋒,  張森林

劉妹琴, 顏鋼鋒, 張森林. 基于LMI方法的時滯BAM神經(jīng)網(wǎng)絡(luò)的全局穩(wěn)定性分析[J]. 電子與信息學(xué)報, 2004, 26(8): 1237-1244.
引用本文: 劉妹琴, 顏鋼鋒, 張森林. 基于LMI方法的時滯BAM神經(jīng)網(wǎng)絡(luò)的全局穩(wěn)定性分析[J]. 電子與信息學(xué)報, 2004, 26(8): 1237-1244.
Liu Mei-qin, Yan Gang-feng, Zhang Sen-lin. Globally Asymptotical Stability Analysis of BAM Neural Networks with Time Delays via LMI Approach[J]. Journal of Electronics & Information Technology, 2004, 26(8): 1237-1244.
Citation: Liu Mei-qin, Yan Gang-feng, Zhang Sen-lin. Globally Asymptotical Stability Analysis of BAM Neural Networks with Time Delays via LMI Approach[J]. Journal of Electronics & Information Technology, 2004, 26(8): 1237-1244.

基于LMI方法的時滯BAM神經(jīng)網(wǎng)絡(luò)的全局穩(wěn)定性分析

Globally Asymptotical Stability Analysis of BAM Neural Networks with Time Delays via LMI Approach

  • 摘要: 對于時滯雙向聯(lián)想記憶(DBAM)神經(jīng)網(wǎng)絡(luò)的平衡點的穩(wěn)定性問題，目前人們已經(jīng)得到了很多富有意義的成果。該文提出一種新的神經(jīng)網(wǎng)絡(luò)模型標(biāo)準(zhǔn)神經(jīng)網(wǎng)絡(luò)模型(SNNM)，通過狀態(tài)的線性變換，將DBAM神經(jīng)網(wǎng)絡(luò)轉(zhuǎn)化為時滯SNNM(DSNNM)，并利用有關(guān)DSNNM的穩(wěn)定性的一些結(jié)論，得到DBAM神經(jīng)網(wǎng)絡(luò)平衡點的全局漸近穩(wěn)定性的充分條件。這些條件都以線性矩陣不等式(LMI)的形式給出，容易驗證，保守性低。該方法擴展了以前的穩(wěn)定性結(jié)果，同時也適用于其它類型的遞歸神經(jīng)網(wǎng)絡(luò)(時滯或非時滯)的穩(wěn)定性分析。
    Abstract: So far many fruitful results have been obtained for stability of equilibrium points of Bidirectional Associative Memory (BAM) neural networks with axonal signal transmission delays (DBAM). A novel neural network model named as Standard Neural Network Model (SNNM) is advanced. By using state affine transformation, the DBAM neural networks arc converted to SNNMs with time delays (DSNNMs). Based on some results of DSNNMs stability, some sufficient conditions for the globally asymptotical stability of DBAM neural networks are derived, which are formulated as linear matrix inequalities (LMIs), which can be verified easily and whose conservativeness is lower. The approach proposed extends the known stability results, and can also be applied to other forms of Recurrent Neural Networks (RNNs) with (or without) time delays.
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  • Kosko B.Adaptive bidirectional associative memories[J].Appl.Opt.1987,26(23):4947-4960[2]廖曉昕.動力系統(tǒng)的穩(wěn)定性理論和應(yīng)用.北京:國防工業(yè)出版社,2000,186-214.[3]Liao X X,Liao Y,Liao Yu.Qualitative analysis of bidirectional associative memory neural networks.Journal of Electronics(China).1998,15(3):208-214.[4]Liao X X,Liao Y,Liao Yu.Stability of bidirectional associative memory neural networks with delays.Journal of Electronics(China).1998,15(4):373-377.[5]Liao X F,Yu J B,Chen G Y.Novel stability criteria for bidirectional associative memory neural networks with time delays[J].International Journal of Circuit Theory and Applications.2002,30(5):519-546[6]Wu Z F,Liao X F.New stability conditions for BAM neural networks with time delays.The 2000IEEE Asia-Pacific Conference on Circuits and Systems,Tianjin,China,Dec.2000:323-326.[7]廖曉峰,劉光遠,虞厥邦.具有軸突信號傳輸延遲的雙向聯(lián)想記憶神經(jīng)網(wǎng)絡(luò).電子科學(xué)學(xué)刊,1997,19(4):439-444.[8]Liao X F,Chen G Y,Edgar N Sanchez.Delayed-dependent exponential stability analysis of delayed neural networks:an LMI approach[J].Neural Networks.2002,15(7):855-866[9]Moore J B,Anderson B D O.A generalization of the Popov criterion[J].Journal of the Franklin Institute.1968,285(6):488-492[10]Boyd S P,Ghaoui L E,Feron E,Balakrishnan V.Linear matrix inequalities in system and control theory.Philadelphia,PA:SIAM,1994:23-24.[11]Barabanov N E,Prokhorov D V.Stability analysis of discrete-time recurrent neural networks[J].IEEE Trans.on Neural Networks.2002,13(2):292-303[12]Gahinet P,Nemirovski A,Laub A J,Chilali M.LMI Control Toolbox.The Math Works Inc.,1995.[13]劉妹琴,張森林.一類離散遞歸神經(jīng)網(wǎng)絡(luò)的穩(wěn)定性分析-LMI方法.浙江大學(xué)學(xué)報(工學(xué)版),2003,37(1):19-23.
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出版歷程
  • 收稿日期:  2003-01-21
  • 修回日期:  2003-09-08
  • 刊出日期:  2004-08-19

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