Multiple ψ-Type Stability and Its Robustness for Recurrent Neural Networks With Time-Varying Delays

被引：26
作者：
Zhang, Fanghai [1 ]
Zeng, Zhigang [1 ]
机构：
[1] Huazhong Univ Sci & Technol, Guangdong Prov Key Lab Digital Mfg Equipment, Key Lab Image Proc & Intelligent Control Educ,Sch, Guangdong HUST Ind Technol Res Inst,Minist China, Wuhan 430074, Hubei, Peoples R China
来源：
IEEE TRANSACTIONS ON CYBERNETICS | 2019年 / 49卷 / 05期
关键词：
Multiple psi-type stability; recurrent neural networks (RNNs); robustness; time-varying delays; GLOBAL EXPONENTIAL STABILITY; LINEAR ACTIVATION FUNCTIONS; ASYMPTOTIC STABILITY; LAGRANGE STABILITY; MU-STABILITY; FINITE-TIME; MULTISTABILITY; CONVERGENCE; SYNCHRONIZATION; SYSTEMS;
D O I：
10.1109/TCYB.2018.2813979
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this paper, the psi-type stability and robustness of recurrent neural networks are investigated by using the differential inequality. By utilizing psi-type functions combined with the inequality techniques, some sufficient conditions ensuring psi-type stability and robustness are derived for linear neural networks with time-varying delays. Then, by choosing appropriate Lipschitz coefficient in subregion, some algebraic criteria of the multiple psi-type stability and robust boundedness are established for the delayed neural networks with time-varying delays. For special cases, several criteria are also presented by selecting parameters with easy implementation. The derived results cover both psi-type mono-stability and multiple psi-type stability. In addition, these theoretical results contain exponential stability, polynomial stability, and mu-stability, and they also complement and extend some previous results. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed criteria.
引用
收藏
页码：1803 / 1815
页数：13
相关论文
共 55 条
[11]   New Conditions for Global Asymptotic Stability of Memristor Neural Networks [J].
Di Marco, Mauro ;
Forti, Mauro ;
Pancioni, Luca .
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, 2018, 29 (05) :1822-1834
[12]   Convergence and Multistability of Nonsymmetric Cellular Neural Networks With Memristors [J].
Di Marco, Mauro ;
Forti, Mauro ;
Pancioni, Luca .
IEEE TRANSACTIONS ON CYBERNETICS, 2017, 47 (10) :2970-2983
[13]   Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations [J].
Di Marco, Mauro ;
Forti, Mauro ;
Nistri, Paolo ;
Pancioni, Luca .
IEEE TRANSACTIONS ON CYBERNETICS, 2016, 46 (11) :2509-2520
[14]   Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube [J].
Di Marco, Mauro ;
Forti, Mauro ;
Grazzini, Massimo ;
Pancioni, Luca .
NEURAL NETWORKS, 2014, 54 :38-48
[15]   Convergence of a Class of Cooperative Standard Cellular Neural Network Arrays [J].
Di Marco, Mauro ;
Forti, Mauro ;
Grazzini, Massimo ;
Pancioni, Luca .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2012, 59 (04) :772-783
[16]   Exponential Stabilization of Memristive Neural Networks via Saturating Sampled-Data Control [J].
Ding, Sanbo ;
Wang, Zhanshan ;
Rong, Nannan ;
Zhang, Huaguang .
IEEE TRANSACTIONS ON CYBERNETICS, 2017, 47 (10) :3027-3039
[17]  
Filippov Aleksei Fedorovich, 1988, Differential Equations with Discontinuous Righthand Sides
[18]   Generalized Lyapunov approach for convergence of neural networks with discontinuous or non-Lipschitz activations [J].
Forti, A ;
Grazzini, A ;
Nistri, P ;
Pancioni, L .
PHYSICA D-NONLINEAR PHENOMENA, 2006, 214 (01) :88-99
[19]   Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain [J].
Forti, M ;
Nistri, P ;
Papini, D .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 2005, 16 (06) :1449-1463
[20]   NEW CONDITIONS FOR GLOBAL STABILITY OF NEURAL NETWORKS WITH APPLICATION TO LINEAR AND QUADRATIC-PROGRAMMING PROBLEMS [J].
FORTI, M ;
TESI, A .
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1995, 42 (07) :354-366
123456