TY - JOUR
T1 - Stability of markovian jump generalized neural networks with interval time-varying delays
AU - Saravanakumar, Ramasamy
AU - Syed Ali, Muhammed
AU - Ahn, Choon Ki
AU - Karimi, Hamid Reza
AU - Shi, Peng
N1 - Funding Information:
Manuscript received October 17, 2015; revised March 29, 2016; accepted April 3, 2016. Date of publication May 9, 2016; date of current version July 18, 2017. This work was supported in part by the National Board for Higher Mathematics–Department of Atomic Energy, New Delhi, under Grant 2/48/10/2011-R&D-II/865 and in part by the National Research Foundation of Korea within the Ministry of Science, ICT & Future Planning under Grant NRF-2014R1A1A1006101. (Corresponding author: Choon Ki Ahn.) R. Saravanakumar and M. Syed Ali are with the Department of Mathematics, Thiruvalluvar University, Vellore 632115, India (e-mail: saravanamaths30@gmail.com; syedgru@gmail.com).
Publisher Copyright:
© 2012 IEEE.
PY - 2017/8
Y1 - 2017/8
N2 - This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.
AB - This paper examines the problem of asymptotic stability for Markovian jump generalized neural networks with interval time-varying delays. Markovian jump parameters are modeled as a continuous-time and finite-state Markov chain. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the linear matrix inequality (LMI) formulation, new delay-dependent stability conditions are established to ascertain the mean-square asymptotic stability result of the equilibrium point. The reciprocally convex combination technique, Jensen's inequality, and the Wirtinger-based double integral inequality are used to handle single and double integral terms in the time derivative of the LKF. The developed results are represented by the LMI. The effectiveness and advantages of the new design method are explained using five numerical examples.
KW - Asymptotic stability
KW - Markovian jump parameters
KW - generalized neural networks (GNNs)
KW - interval time-varying delay
UR - http://www.scopus.com/inward/record.url?scp=85029697064&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2016.2552491
DO - 10.1109/TNNLS.2016.2552491
M3 - Article
C2 - 28113729
AN - SCOPUS:85029697064
SN - 2162-237X
VL - 28
SP - 1840
EP - 1850
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 8
M1 - 7466838
ER -