Linear Threshold Discrete-Time Recurrent Neural Networks: Stability and Globally Attractive Sets

被引：12
作者：
Shen, Tao [1 ]
Petersen, Ian R. [2 ]
机构：
[1] Univ Jinan, Sch Elect Engn, Jinan 250022, Peoples R China
[2] Australian Def Force Acad, Univ New South Wales, Sch Engn & Informat Technol, Canberra, ACT 2600, Australia
来源：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 09期
基金：
澳大利亚研究理事会; 中国国家自然科学基金;
关键词：
Completely stable systems; globally attractive sets; invariant sets; linear matrix inequalities; neural networks; INVARIANT-SETS; COMPUTATION; SYSTEMS; BOUNDS;
D O I：
10.1109/TAC.2015.2503360
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The stability of linear threshold dynamic neural networks is studied, and a series of methods to obtain globally attractive sets is proposed. A sufficient condition to judge whether an invariant set is a globally attractive set is also proposed. This method requires only the solution to a class of linear matrix inequalities. Also, two direct methods to obtain globally attractive sets are given. The stability criteria presented are based on the proposed globally attractive sets. Some numerical examples are given to illustrate the effectiveness of the obtained results.
引用
收藏
页码：2650 / 2656
页数：7
相关论文
共 38 条
[1]   Frustration, stability, and delay-induced oscillations in a neural network model [J].
Belair, J ;
Campbell, SA ;
VandenDriessche, P .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1996, 56 (01) :245-255
[2]   Set invariance in control [J].
Blanchini, F .
AUTOMATICA, 1999, 35 (11) :1747-1767
[3]  
Blanchini F, 2008, SYST CONTROL-FOUND A, P1
[4]   AN INTEGRAL-INVARIANCE PRINCIPLE FOR NONLINEAR-SYSTEMS [J].
BYRNES, CI ;
MARTIN, CF .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (06) :983-994
[5]   CELLULAR NEURAL NETWORKS - THEORY [J].
CHUA, LO ;
YANG, L .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1988, 35 (10) :1257-1272
[6]   RECURRENT EXCITATION IN NEOCORTICAL CIRCUITS [J].
DOUGLAS, RJ ;
KOCH, C ;
MAHOWALD, M ;
MARTIN, KAC ;
SUAREZ, HH .
SCIENCE, 1995, 269 (5226) :981-985
[7]   On neurodynamics with limiter function and Linsker's developmental model [J].
Feng, JF ;
Pan, H ;
Roychowdhury, VP .
NEURAL COMPUTATION, 1996, 8 (05) :1003-1019
[8]   NECESSARY AND SUFFICIENT CONDITION FOR ABSOLUTE STABILITY OF NEURAL NETWORKS [J].
FORTI, M ;
MANETTI, S ;
MARINI, M .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1994, 41 (07) :491-494
[9]   Permitted and forbidden sets in symmetric threshold-linear networks [J].
Hahnloser, RHR ;
Seung, HS ;
Slotine, JJ .
NEURAL COMPUTATION, 2003, 15 (03) :621-638
[10]   Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit [J].
Hahnloser, RHR ;
Sarpeshkar, R ;
Mahowald, MA ;
Douglas, RJ ;
Seung, HS .
NATURE, 2000, 405 (6789) :947-951
1234