TY - JOUR
T1 - Exponential stability, passivity, and dissipativity analysis of generalized neural networks with mixed time-varying delays
AU - Saravanakumar, R.
AU - Rajchakit, Grienggrai
AU - Ahn, Choon Ki
AU - Karimi, Hamid Reza
N1 - Funding Information:
Manuscript received October 5, 2016; revised March 15, 2017; accepted June 15, 2017. Date of publication July 13, 2017; date of current version January 6, 2019. This work was supported in part by the Thailand Research Fund and in part by the National Research Foundation of Korea funded by the Ministry of Science, ICT and Future Planning under Grant NRF-2017R1A1A1A05001325. This paper was recommended by Associate Editor A. H. Tan. (Corresponding author: Choon Ki Ahn.) R. Saravanakumar is with the Department of Mathematics, Faculty of Science, Mahidol University, Bangkok 10400, Thailand, and also with the Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand (e-mail: saravanamaths30@gmail.com).
Publisher Copyright:
© 2013 IEEE.
PY - 2019/2
Y1 - 2019/2
N2 - In this paper, we analyze the exponential stability, passivity, and $\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ - $\boldsymbol {\gamma }$ -dissipativity of generalized neural networks (GNNs) including mixed time-varying delays in state vectors. Novel exponential stability, passivity, and $\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ - $\boldsymbol {\gamma }$ -dissipativity criteria are developed in the form of linear matrix inequalities for continuous-time GNNs by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and applying a new weighted integral inequality for handling integral terms in the time derivative of the established LKF for both single and double integrals. Some special cases are also discussed. The superiority of employing the method presented in this paper over some existing methods is verified by numerical examples.
AB - In this paper, we analyze the exponential stability, passivity, and $\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ - $\boldsymbol {\gamma }$ -dissipativity of generalized neural networks (GNNs) including mixed time-varying delays in state vectors. Novel exponential stability, passivity, and $\boldsymbol {(\mathfrak {Q},\mathfrak {S},\mathfrak {R})}$ - $\boldsymbol {\gamma }$ -dissipativity criteria are developed in the form of linear matrix inequalities for continuous-time GNNs by constructing an appropriate Lyapunov-Krasovskii functional (LKF) and applying a new weighted integral inequality for handling integral terms in the time derivative of the established LKF for both single and double integrals. Some special cases are also discussed. The superiority of employing the method presented in this paper over some existing methods is verified by numerical examples.
KW - (Q, S, R)-γ-dissipativity
KW - Exponential passivity
KW - Generalized neural networks (GNNs)
KW - Time-varying delay
KW - Weighted integral inequality (WII)
UR - http://www.scopus.com/inward/record.url?scp=85028950307&partnerID=8YFLogxK
U2 - 10.1109/TSMC.2017.2719899
DO - 10.1109/TSMC.2017.2719899
M3 - Article
AN - SCOPUS:85028950307
SN - 2168-2216
VL - 49
SP - 395
EP - 405
JO - IEEE Transactions on Systems, Man, and Cybernetics: Systems
JF - IEEE Transactions on Systems, Man, and Cybernetics: Systems
IS - 2
M1 - 7979548
ER -