Finite-time Stability, Dissipativity and Passivity Analysis of Discrete-time Neural Networks Time-varying Delays

Porpattama Hammachukiattikul

Abstract


The neural network time-varying delay was described as the dynamic properties of a neural cell, including neural functional and neural delay differential equations. The differential expression explains the derivative term of current and past state. The objective of this paper obtained the neural network time-varying delay. A delay-dependent condition is provided to ensure the considered discrete-time neural networks with time-varying delays to be finite-time stability, dissipativity, and passivity. This paper using a new Lyapunov-Krasovskii functional as well as the free-weighting matrix approach and a linear matrix inequality analysis (LMI) technique constructing to a novel sufficient criterion on finite-time stability, dissipativity, and passivity of the discrete-time neural networks with time-varying delays for improving. We propose sufficient conditions for discrete-time neural networks with time-varying delays. An effective LMI approach derives by base the appropriate type of Lyapunov functional. Finally, we present the effectiveness of novel criteria of finite-time stability, dissipativity, and passivity condition of discrete-time neural networks with time-varying delays in the form of linear matrix inequality (LMI).

Keywords


Finite-time Stability; Dissipativity and Passivity Analysis; Lyapunov-Krasovskii Functional.

References


Haykin, S. "Neural Networks: A Comprehensive Foundation, Prentice Hall PTR." Upper Saddle River, NJ, USA (1998).

Wangli He, and Jinde Cao. “Exponential Synchronization of Hybrid Coupled Networks with Delayed Coupling.” IEEE Transactions on Neural Networks 21, no. 4 (April 2010): 571–583. doi:10.1109/tnn.2009.2039803.

Popov, Vasile Mihai, and Radu Georgescu. "Hyperstability of control systems." Springer-Verlag, 1973.

Willems, J.C., Dissipative dynamical systems part I: general theory, Arch. Ration. Mech. Anal. 45 (5) (1972) 321-351. doi:10.1109/9780470544334.ch20.

Zhang, Dan, and Li Yu. “Exponential State Estimation for Markovian Jumping Neural Networks with Time-Varying Discrete and Distributed Delays.” Neural Networks 35 (November 2012): 103–111. doi:10.1016/j.neunet.2012.08.005.

Dan Zhang, Li Yu, Qing-Guo Wang, and Chong-Jin Ong. “Estimator Design for Discrete-Time Switched Neural Networks With Asynchronous Switching and Time-Varying Delay.” IEEE Transactions on Neural Networks and Learning Systems 23, no. 5 (May 2012): 827–834. doi:10.1109/tnnls.2012.2186824.

Chen, Guoliang, Jianwei Xia, Ju H. Park, and Guangming Zhuang. “New Delay-Dependent Global Robust Passivity Analysis for Stochastic Neural Networks with Markovian Jumping Parameters and Interval Time-Varying Delays.” Complexity 21, no. 6 (April 8, 2015): 167–179. doi:10.1002/cplx.21677.

Raja, R., and R. Samidurai. “New Delay Dependent Robust Asymptotic Stability for Uncertain Stochastic Recurrent Neural Networks with Multiple Time Varying Delays.” Journal of the Franklin Institute 349, no. 6 (August 2012): 2108–2123. doi:10.1016/j.jfranklin.2012.03.007.

Shi, Kaibo, Hong Zhu, Shouming Zhong, Yong Zeng, and Yuping Zhang. “New Stability Analysis for Neutral Type Neural Networks with Discrete and Distributed Delays Using a Multiple Integral Approach.” Journal of the Franklin Institute 352, no. 1 (January 2015): 155–176. doi:10.1016/j.jfranklin.2014.10.005.

Zeng, Hong-Bing, Ju H. Park, Chang-Fan Zhang, and Wei Wang. “Stability and Dissipativity Analysis of Static Neural Networks with Interval Time-Varying Delay.” Journal of the Franklin Institute 352, no. 3 (March 2015): 1284–1295. doi:10.1016/j.jfranklin.2014.12.023.

Mohamad, S., and K. Gopalsamy. “Exponential Stability of Continuous-Time and Discrete-Time Cellular Neural Networks with Delays.” Applied Mathematics and Computation 135, no. 1 (February 2003): 17–38. doi:10.1016/s0096-3003(01)00299-5.

Q.C. Zhong, Robust Control of Time-Delay Systems, Springer-Verlag, London, 2006.

M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1993.

J. Sarangapani, Neural Network Control of Nonlinear Discrete-Time Systems, Taylor and Francis Group, Boca Raton, London, New York, 2006.

J.C. Willems, The Analysis of Feedback Systems, The MIT Press, Cambridge, 1971.

W.M. Hadda, V.S. Chellaboina, Nonlinear Dynamical Systems and Control: A Lyapunov-based Approach, Princeton University Press, USA, 2008.

Shen, Hao, Ju H. Park, Lixian Zhang, and Zheng-Guang Wu. “Robust Extended Dissipative Control for Sampled-Data Markov Jump Systems.” International Journal of Control 87, no. 8 (February 26, 2014): 1549–1564. doi:10.1080/00207179.2013.878478.

Shen, Hao, Yanzheng Zhu, Lixian Zhang, and Ju H. Park. “Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links.” IEEE Transactions on Neural Networks and Learning Systems 28, no. 2 (February 2017): 346–358. doi:10.1109/tnnls.2015.2511196.

D. Hill, P. Moylan, The stability of nonlinear dissipative systems, IEEE Trans. Autom. Control 21 (5) (1976) 708-711.

Shen, Hao, Zheng-Guang Wu, and Ju H. Park. “Reliable Mixed Passive and ℋ∞ Filtering for Semi-Markov Jump Systems with Randomly Occurring Uncertainties and Sensor Failures.” International Journal of Robust and Nonlinear Control 25, no. 17 (October 15, 2014): 3231–3251. doi:10.1002/rnc.3255.

Shen, Hao, Zheng-Guang Wu, Ju H. Park, and Zhengqiang Zhang. “Extended Dissipativity-Based Synchronization of Uncertain Chaotic Neural Networks with Actuator Failures.” Journal of the Franklin Institute 352, no. 4 (April 2015): 1722–1738. doi:10.1016/j.jfranklin.2015.01.026.

Zheng-Guang Wu, Peng Shi, Hongye Su, and Jian Chu. “Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays.” IEEE Transactions on Neural Networks 22, no. 10 (October 2011): 1566–1575. doi:10.1109/tnn.2011.2163203.

Zheng-Guang Wu, Peng Shi, Hongye Su, and Jian Chu. “Dissipativity Analysis for Discrete-Time Stochastic Neural Networks With Time-Varying Delays.” IEEE Transactions on Neural Networks and Learning Systems 24, no. 3 (March 2013): 345–355. doi:10.1109/tnnls.2012.2232938.

Zeng, Hong-Bing, Ju H. Park, and Hao Shen. “Robust Passivity Analysis of Neural Networks with Discrete and Distributed Delays.” Neurocomputing 149 (February 2015): 1092–1097. doi:10.1016/j.neucom.2014.07.024.

Zeng, Hong-Bing, Ju H. Park, Chang-Fan Zhang, and Wei Wang. “Stability and Dissipativity Analysis of Static Neural Networks with Interval Time-Varying Delay.” Journal of the Franklin Institute 352, no. 3 (March 2015): 1284–1295. doi:10.1016/j.jfranklin.2014.12.023.

Zhang, Baoyong, Shengyuan Xu, and James Lam. “Relaxed Passivity Conditions for Neural Networks with Time-Varying Delays.” Neurocomputing 142 (October 2014): 299–306. doi:10.1016/j.neucom.2014.04.031.

Zeng, Hong-Bing, Yong He, Min Wu, and Shen-Ping Xiao. “Passivity Analysis for Neural Networks with a Time-Varying Delay.” Neurocomputing 74, no. 5 (February 2011): 730–734. doi:10.1016/j.neucom.2010.09.020.

Li, Ning, and Wei Xing Zheng. “Passivity Analysis for Quaternion-Valued Memristor-Based Neural Networks with Time-Varying Delay.” IEEE Transactions on Neural Networks and Learning Systems (2019): 1–12. doi:10.1109/tnnls.2019.2908755.

Zeng, Hong-Bing, Yong He, Min Wu, and Hui-Qin Xiao. “Improved Conditions for Passivity of Neural Networks With a Time-Varying Delay.” IEEE Transactions on Cybernetics 44, no. 6 (June 2014): 785–792. doi:10.1109/tcyb.2013.2272399.

Kang, Wei, and Shouming Zhong. “Passivity Analysis of Discrete-Time Memristive Neural Networks with Time-Varying Delay.” 2017 9th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC) (August 2017). doi:10.1109/ihmsc.2017.177.

Park, M.J., O.M. Kwon, and J.H. Ryu. “Passivity and Stability Analysis of Neural Networks with Time-Varying Delays via Extended Free-Weighting Matrices Integral Inequality.” Neural Networks 106 (October 2018): 67–78. doi:10.1016/j.neunet.2018.06.010.

Chen, Yonggang, Shumin Fei, and Yongmin Li. “Improved Delay-Dependent Stability Conditions for Recurrent Neural Networks with Multiple Time-Varying Delays.” Nonlinear Dynamics 78, no. 2 (June 24, 2014): 803–812. doi:10.1007/s11071-014-1478-y.

Liu, Pin-Lin. “Improved Delay-Derivative-Dependent Stability Analysis for Generalized Recurrent Neural Networks with Interval Time-Varying Delays.” Neural Processing Letters (August 10, 2019). doi:10.1007/s11063-019-10088-8.

Wang, Liyan, Yang Wang, and Jianxia Liu. “Delay - Dependent Robust Stability of Neural Networks with Time-Varying Delays.” 2018 Chinese Control and Decision Conference (CCDC) (June 2018). doi:10.1109/ccdc.2018.8407796.

Liu, Yurong, Zidong Wang, and Xiaohui Liu. “Global Exponential Stability of Generalized Recurrent Neural Networks with Discrete and Distributed Delays.” Neural Networks 19, no. 5 (June 2006): 667–675. doi:10.1016/j.neunet.2005.03.015.

Zheng-Guang Wu, Peng Shi, Hongye Su, and Jian Chu. “Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks with Mixed Time Delays.” IEEE Transactions on Neural Networks 22, no. 10 (October 2011): 1566–1575. doi:10.1109/tnn.2011.2163203.

Bo Zhou, and Qiankun Song. “Boundedness and Complete Stability of Complex-Valued Neural Networks with Time Delay.” IEEE Transactions on Neural Networks and Learning Systems 24, no. 8 (August 2013): 1227–1238. doi:10.1109/tnnls.2013.2247626.

Wang, Feng-Xian, Xin-Ge Liu, Mei-Lan Tang, and Yan-Jun Shu. “Stability Analysis of Discrete-Time Systems with Variable Delays via Some New Summation Inequalities.” Advances in Difference Equations 2016, no. 1 (April 5, 2016). doi:10.1186/s13662-016-0829-z.


Full Text: PDF

DOI: 10.28991/esj-2019-01198

Refbacks

  • There are currently no refbacks.


Copyright (c) 2019 Porpattama Hammachukiattikul