This paper investigates the issue of finite time stability analysis of time-delayed neural networks by introducing a new Lyapunov functional which uses the information on the delay sufficiently and an augmented Lyapunov functional which contains some triple integral terms. Some improved delay-dependent stability criteria are derived using Jensen's inequality, reciprocally convex combination methods. Then, the finite-time stability conditions are solved by the linear matrix inequalities (LMIs). Numerical examples are finally presented to verify the effectiveness of the obtained results.
Issue Section:
Research Papers
References
1.
Balasubramaniam
, P.
, Ali
, M. S.
, and Arik
, S.
, 2010
, “Global Asymptotic Stability of Stochastic Fuzzy Cellular Neural Networks With Multiple Time-Varying Delays
,” Expert Syst. Appl.
, 37
(12
), pp. 7737
–7744
.2.
Zhou
, X.
, Tian
, J.
, Ma
, H.
, and Zhong
, S.
, 2014
, “Improved Delay-Dependent Stability Criteria for Recurrent Neural Networks With Time-Varying Delays
,” Neurocomputing
, 129
, pp. 401
–408
.3.
Hua
, C.
, Long
, C.
, and Guan
, X.
, 2006
, “New Results on Stability Analysis of Neural Networks With Time-Varying Delays
,” Phys. Lett. A
, 352
(4–5
), pp. 335
–340
.4.
He
, Y.
, Liu
, G.
, and Rees
, D.
, 2007
, “New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay
,” IEEE Trans. Neural Networks
, 18
(1
), pp. 310
–314
.5.
Sun
, J.
, Liu
, G.
, Chen
, J.
, and Rees
, D.
, 2009
, “Improved Stability Criteria for Neural Networks With Time-Varying Delay
,” Phys. Lett. A
, 373
(3
), pp. 342
–348
.6.
Tian
, J.
, and Xie
, X.
, 2010
, “New Asymptotic Stability Criteria for Neural Networks With Time-Varying Delay
,” Phys. Lett. A
, 374
(7
), pp. 938
–943
.7.
Tian
, J.
, Xiong
, W.
, and Xu
, F.
, 2014
, “Improved Delay-Partitioning Method to Stability Analysis for Neural Networks With Discrete and Distributed Time-Varying Delays
,” Appl. Math. Comput.
, 233
, pp. 152
–164
.8.
Shi
, K.
, Zhong
, S.
, Zhu
, H.
, Liu
, X.
, and Zeng
, Y.
, 2015
, “New Delay-Dependent Stability Criteria for Neutral-Type Neural Networks With Mixed Random Time-Varying Delays
,” Neurocomputing
, 168
, pp. 896
–907
.9.
Qiao
, H.
, Peng
, J.
, Xu
, Z.-B.
, and Zhang
, B.
, 2003
, “A Reference Model Approach to Stability Analysis of Neural Networks
,” IEEE Trans. Syst., Man, Cybern., Part B (Cybern.)
, 33
(6
), pp. 925
–936
.10.
Shi
, K.
, Zhu
, H.
, Zhong
, S.
, Zeng
, Y.
, and Zhang
, Y.
, 2015
, “New Stability Analysis for Neutral Type Neural Networks With Discrete and Distributed Delays Using a Multiple Integral Approach
,” J. Franklin Inst.
, 352
(1
), pp. 155
–176
.11.
Hou
, L.
, Zong
, G.
, and Wu
, Y.
, 2011
, “Robust Exponential Stability Analysis of Discrete-Time Switched Hopfield Neural Networks With Time Delay
,” Nonlinear Anal.: Hybrid Syst.
, 5
(3
), pp. 525
–534
.12.
Zhu
, Q.
, Cao
, J.
, and Rakkiyappan
, R.
, 2015
, “Exponential Input-to-State Stability of Stochastic Cohen–Grossberg Neural Networks With Mixed Delays
,” Nonlinear Dyn.
, 79
(2
), pp. 1085
–1098
.13.
Syed Ali
, M.
, 2015
, “Stability of Markovian Jumping Recurrent Neural Networks With Discrete and Distributed Time-Varying Delays
,” Neurocomputing
, 149
(Pt. C
), pp. 1280
–1285
.14.
Balasubramaniam
, P.
, and Vembarasan
, V.
, 2011
, “Asymptotic Stability of BAM Neural Networks of Neutral-Type With Impulsive Effects and Time Delay in the Leakage Term
,” Int. J. Comput. Math.
, 88
(15
), pp. 3271
–3291
.15.
Dorato
, P.
, 1961
, “Short-Time Stability in Linear Time-Varying Systems
,” Polytechnic Institute of Brooklyn, Brooklyn, NY, Technical, Report No. PIBMRI-908-61
.16.
Weiss
, L.
, and Infante
, E.
, 1967
, “Finite Time Stability Under Perturbing Forces and on Product Spaces
,” IEEE Trans. Autom. Control
, 12
(1
), pp. 54
–59
.17.
Michel
, A.
, and Porter
, D.
, 1972
, “Practical Stability and Finite-Time Stability of Discontinuous Systems
,” IEEE Trans. Circuit Theory
, 19
(2
), pp. 123
–129
.18.
Syed Ali
, M.
, Saravanan
, S.
, and Zhu
, Q.
, 2017
, “Non-Fragile Finite-Time H∞ State Estimation of Neural Networks With Distributed Time-Varying Delay
,” J. Franklin Inst.
, 354
(16
), pp. 7566
–7584
.19.
Syed Ali
, M.
, Saravanan
, S.
, and Zhu
, Q.
, 2017
, “Finite-Time Stability of Neutral-Type Neural Networks With Random Time-Varying Delays
,” Int. J. Syst. Sci.
, 48
(15
), pp. 3279
–3295
.20.
Syed Ali
, M.
, and Saravanan
, S.
, 2017
, “Finite-Time Stability for Memristor Based Uncertain Neural Networks With Time-Varying Delays-Via Average Dwell Time Approach
,” Chin. J. Phys.
, 55
(5
), pp. 1953
–1971
.21.
Zhang
, Y.
, Shi
, P.
, Nguang
, S. K.
, Zhang
, J.
, and Karimi
, H. R.
, 2014
, “Finite-Time Boundedness for Uncertain Discrete Neural Networks With Time-Delays and Markovian Jumps
,” Neurocomputing
, 140
, pp. 1
–7
.22.
Syed Ali
, M.
, Saravanan
, S.
, and Arik
, S.
, 2016
, “Finite-Time H∞ State Estimation for Switched Neural Networks With Time-Varying Delays
,” Neurocomputing
, 207
, pp. 580
–589
.23.
Xing
, X.
, Yao
, D.
, Lu
, Q.
, and Li
, X.
, 2015
, “Finite-Time Stability of Markovian Jump Neural Networks With Partly Unknown Transition Probabilities
,” Neurocomputing
, 159
, pp. 282
–287
.24.
Cheng
, J.
, Zhong
, S.
, Zhong
, Q.
, Zhu
, H.
, and Du
, Y.
, 2014
, “Finite-Time Boundedness of State Estimation for Neural Networks With Time-Varying Delays
,” Neurocomputing
, 129
, pp. 257
–264
.25.
Syed Ali
, M.
, and Saravanan
, S.
, 2016
, “Robust Finite-Time H∞ Control for a Class of Uncertain Switched Neural Networks of Neutral-Type With Distributed Time Varying Delays
,” Neurocomputing
, 177
, pp. 454
–468
.26.
Cheng
, J.
, Zhu
, H.
, Zhong
, S.
, Zeng
, Y.
, and Hou
, L.
, 2014
, “Finite-Time H∞ Filtering for a Class of Discrete-Time Markovian Jump Systems With Partly Unknown Transition Probabilities
,” Int. J. Adapt. Control Signal Process.
, 28
(10
), pp. 1024
–1042
.27.
Park
, P.
, Ko
, J. W.
, and Jeong
, C.
, 2011
, “Reciprocally Convex Approach to Stability of Systems With Time-Varying Delays
,” Automatica
, 47
(1
), pp. 235
–238
.28.
Gu
, K.
, Chen
, J.
, and Kharitonov
, V. L.
, 2003
, Stability of Time-Delay Systems
, Springer Science & Business Media
, New York.29.
Cao
, J.-D.
, 2000
, “Global Asymptotic Stability of Neural Networks With Transmission Delays
,” Int. J. Syst. Sci.
, 31
(10
), pp. 1313
–1316
.30.
Liu
, Y.
, Wang
, Z.
, and Liu
, X.
, 2006
, “Global Exponential Stability of Generalized Recurrent Neural Networks With Discrete and Distributed Delays
,” Neural Networks
, 19
(5
), pp. 667
–675
.31.
Ordaz
, P.
, Santos-Sánchez
, O.-J.
, Rodríguez-Guerrero
, L.
, and González-Facundo
, A.
, 2017
, “Nonlinear Stabilization for a Class of Time Delay Systems Via Inverse Optimality Approach
,” ISA Trans.
, 67
, pp. 1
–8
.Copyright © 2018 by ASME
You do not currently have access to this content.
