Abstract
This paper is concerned with the exponential H ∞ filtering problem for a class of discrete-time switched neural networks with random time-varying delays based on the sojourn-probability-dependent method. Using the average dwell time approach together with the piecewise Lyapunov function technique, sufficient conditions are proposed to guarantee the exponential stability for the switched neural networks with random time-varying delays which are characterized by introducing a Bernoulli stochastic variable. Based on the derived H ∞ performance analysis results, the H ∞ filter design is formulated in terms of Linear Matrix Inequalities (LMIs). Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design procedure.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Kwon O M, Park J H. New delay-dependent robust stability criteria for uncertain neural networks with time-varying delay. Appl Math Comput, 2008, 205: 417–427
Cao J, Wang J. Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delay. Neural Networks, 2004, 17: 379–390
Arik S. An analysis of exponential stability of delayed neural networks with time-varying delays. Neural Networks, 2004, 17: 1027–1031
Zhang H, Liu Z, Huang G. Novel delay-dependent robust stability analysis for switched neutral-type neural networks with time-varying delays via SC technique. IEEE T Syst Cy, 2010, 40: 1480–1491
Song Z, Xu J. Stability switches and Bogdanov-Takens bifurcation in an inertial two-neuron coupling system with multiple delays. Sci China Tech Sci, 2014, 57: 893–904
Jiao X, Zhu D. Phase-response synchronization in neuronal population. Sci China Tech Sci, 2014, 57: 923–928
Qin H, Ma J, Jin W, et al. Dynamics of electric activities in neuron and neurons of network induced by autapses. Sci China Tech Sci, 2014, 57: 936–946
Song X, Wang C, Ma J, et al. Transition of electric activity of neurons induced by chemical and electric autapses. Sci China Tech Sci, 2015, 58: 1007–1014
Cao J, Sivasamy R, Rakkiyappan R. Sampled-Data H ∞ synchronization of Chaotic Lur’e systems with time delay. Circ Syst Signal Pr, 2015, doi: 10.1007/s00034-015-0105-6
Rakkiyappan R, Sakthivel N, Cao J. Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Neural Networks, 2015, 66: 46–63
Wu L, Zheng W X. Weighted H ∞ model reduction for linear switched systems with time-varying delay. Automatica, 2009, 45: 186–193
Sun Z, Ge S. Stability Theory of Switched Dynamical Systems. Springer Verlag, 2011
Jeong C, Park P, Kim S H. Improved approach to robust stability and H ∞ performance analysis for systems with an interval time-varying delay. Appl Math Comput, 2012, 218: 10533–10541
Wei G, Wang Z, Lam J, et al. Robust filtering for stochastic genetic regulatory networks with time-varying delay. Math Biosci, 2009, 220: 73–80
Balasubramaniam P, Krishnasamy R, Rakkiyappan R. Delaydependent stability of neutral systems with time varying delays using delay-decomposition approach. Appl Math Model, 2012, 36: 2253–2261
Liang J, Wang Z, Liu X. State estimation for coupled uncertain stochastic networks with missing measurements and time varying delays: The discrete case. IEEE T Neural Networ, 2009, 20: 781–793
Lakshmanan S, Park J H, Jung H Y, et al. Design of state estimator for neural networks with leakage, discrete and distributed delays. Appl Math Comput, 2012, 218: 11297–11310
Kwon O M, Park M J, Lee S M, et al. Stability for neural networks with time-varying delaying via some new approaches. IEEE T Neural Networ, 2013, 24: 181–193
Kwon O M, Lee S M, Park J H, et al. New approaches on stability criteria for neural networks with interval time-varying delays. Appl Math Comput, 2012, 218: 9953–9964
Kim D K, Park P G, Ko J W. Output-feedback H ∞ control of systems over communication networks using deterministic switching system approach. Automatica, 2004, 40: 1205–1212
Wu L, Zhiguang F, Lam J. Stability and synchronization of discretetime neural networks with switching parameters and time-varying delays. IEEE T Neural Networ, 2013, 24: 1957–1972
Wu X, Tang Y, Zhang W. Stability analysis of switched stochastic neural networks with time-varying delays. Neural Networks, 2014, 51: 39–49
Ishii H, Francis B A. Stabilizing a linear system by switching control with dwell time. IEEE T Automat Cont, 2002, 47: 1962–1973
Yao Y, Liang J, Cao J. Stability analysis for switched genetic regulatory networks: An average dwell time approach. J Franklin Inst, 2011, 348: 2718–2733
Wu L, Zheng W X. H ∞ model reduction for switched hybrid systems with time-varying delay. Automatica, 2009, 45: 186–193
Wu L, Feng Z, Zheng W X. Exponential stability analysis for delayed neural networks with switching parameters: average dwell time approach. IEEE T Neural Networ, 2010, 21: 1396–1407
Hu M, Cao J, Hu A. Mean square exponential stability for discretetime stochastic switched static neural networks with randomly occurring nonlinearities and stochastic delay. Neurocomputing, 2014, 129: 476–481
Hou L, Zong G, Wu L. Robust stability analysis of discrete-time switched Hopfield neural networks with time delay. Nonlinear Anal Hybird Syst, 2011, 5: 525–534
Wu Z, Shi P, Su H, et al. Delay dependent exponential stability analysis for discrete-time switched neural networks with time-varying delay. Neurocomputing, 2011, 74: 1626–1631
Mathiyalagan K, Sakthivel R, Marshal Anthoni S. New robust exponential stability results for discrete -time switched fuzzy neural networks with time delays. Computers and Mathematics with Applications, 2012, 64: 2926–2938
Wang Z, Ho D W C, Liu X. State estimation for delayed neural networks. IEEE T Neural Networ, 2005, 16: 279–284
Bao H, Cao J. Delay-distribution-dependent state estimation for discrete time stochastic neural networks with random delay. Neural Networks, 2011, 24: 19–28
Balasubramaniam P, Jarina B L. Robust state estimation for discretetime genetic regulatory network with random delay. Neurocomputing, 2013, 122: 349–369
Tang Y, Fang J, Xia M, et al. Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed timevarying delays. Neurocomputing, 2009, 72: 3830–3838
Zhang Y, Yue D, Tian E. Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay, Neurocomputing, 2009, 72: 1265–1273
Tian E, Wong W K, Yue D. Robust H ∞ control for switched systems with input delays: A sojourn-probability-dependent method. Inform Sci, 2014, 283: 22–35
Tian E, Yue D, Yang T. Analysis and synthesis of randomly switched systems with known sojourn probabilities. Inform Sci, 2014, 277: 481–491
Liu Y, Wang Z, Liu X. Global exponential stability of generalized recurrent neural networks with discrete and distributed delays. Neural Networks, 2006, 19: 667–675
Wang T, Xue M, Fei S, et al. Triple Lyapunov functional technique on delay dependent stability for discrete time dynamical network. Neurocomputing, 2013, 122: 221–228
Park P, Ko J W, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47: 235–238
Boyd B, Ghoui L E, Feron E, et al. Linear matrix inequalities in system and control theory. SIAM, Philadelphia, 1994
Liu J, Zhang J. Note on stability of discrete-time time varying delay system. IET Contr Theor Appl, 2012, 2: 335–339
Wang J, Yang H. Exponential stability of a class of networked control systems with time delays and packet dropouts. Appl Math Comput, 2012, 218: 8887–8894
Zhang L, Boukas E K, Shi P. Exponential H ∞ filtering for uncertain discrete-time switched linear systems with average dwell time: A µ-dependent approach. Int J Robust Nonlin, 2008, 18: 1188–1207
Zhao Y, Gao H, Lam J, et al. Stability and stabilization of delayed TS fuzzy systems: a delay partitioning approach. IEEE T Fuzzy Syst, 2009, 17: 750–762
Yue D, Tian E, Zhang Y, et al. Delay-distribution-dependent robust stability of uncertain systems with time-varying delay. Int J Robust Nonlin, 2009, 19: 377–393
Mathiyalagan K, Su H, Shi P, et al. Exponential H ∞ filtering for discrete-time switched neural networks with random delays. IEEE T Cybern, 2015, 45: 676–687
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cao, J., Rakkiyappan, R., Maheswari, K. et al. Exponential H ∞ filtering analysis for discrete-time switched neural networks with random delays using sojourn probabilities. Sci. China Technol. Sci. 59, 387–402 (2016). https://doi.org/10.1007/s11431-016-6006-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-016-6006-5