TY - JOUR
T1 - Stability and convergence analysis for a class of neural networks
AU - Gao, Xingbao
AU - Liao, Li Zhi
N1 - Funding Information:
Manuscript received February 16, 2011; revised May 29, 2011; accepted September 2, 2011. Date of publication September 29, 2011; date of current version November 2, 2011. This work was supported in part by the National Science Foundation of China under Grant 60671063 and Grant 10902062, the Hong Kong Baptist University, and the Research Grant Council of Hong Kong.
PY - 2011/11
Y1 - 2011/11
N2 - In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.
AB - In this paper, we analyze and establish the stability and convergence of the dynamical system proposed by Xia and Feng, whose equilibria solve variational inequality and related problems. Under the pseudo-monotonicity and other conditions, this system is proved to be stable in the sense of Lyapunov and converges to one of its equilibrium points for any starting point. Meanwhile, the global exponential stability of this system is also shown under some mild conditions without the strong monotonicity of the mapping. The obtained results improve and correct some existing ones. The validity and performance of this system are demonstrated by some numerical examples.
KW - Convergence
KW - exponential stability
KW - neural network
KW - variational inequality
UR - http://www.scopus.com/inward/record.url?scp=80455177011&partnerID=8YFLogxK
U2 - 10.1109/TNN.2011.2167760
DO - 10.1109/TNN.2011.2167760
M3 - Journal article
C2 - 21965201
AN - SCOPUS:80455177011
SN - 1045-9227
VL - 22
SP - 1770
EP - 1782
JO - IEEE Transactions on Neural Networks
JF - IEEE Transactions on Neural Networks
IS - 11
M1 - 6031924
ER -