Robust extended dissipativity criteria for discrete-time uncertain neural networks with time-varying delays

In this draft, we consider the problem of robust extended dissipativity for uncertain discrete-time neural networks (DNNs) with time-varying delays. By constructing appropriate Lyapunov–Krasovskii functional (LKF), sufficient conditions are established to ensure that the considered time-delayed uncertain DNN is extended dissipative. The derived conditions are presented in terms of linear matrix inequalities (LMIs). Numerical examples are provided to illustrate the superiority of this result.

[1]  Hao Shen,et al.  Extended Dissipative State Estimation for Markov Jump Neural Networks With Unreliable Links , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Wei Xing Zheng,et al.  A new approach to stability analysis of discrete-time recurrent neural networks with time-varying delay , 2009, Neurocomputing.

[3]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

[4]  Grienggrai Rajchakit,et al.  Exponential stability of semi-Markovian jump generalized neural networks with interval time-varying delays , 2016, Neural Computing and Applications.

[5]  John Todd,et al.  Discrete analogs of inequalities of Wirtinger , 1955 .

[6]  PooGyeon Park,et al.  Reciprocally convex approach to stability of systems with time-varying delays , 2011, Autom..

[7]  Qian Ma,et al.  Robust passivity analysis of a class of discrete-time stochastic neural networks , 2013, Neural Computing and Applications.

[8]  Hamid Reza Karimi,et al.  Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties , 2009 .

[9]  Ting Wang,et al.  Triple Lyapunov functional technique on delay-dependent stability for discrete-time dynamical networks , 2013, Neurocomputing.

[10]  Zhengwen Tu,et al.  Extended dissipative analysis for memristive neural networks with two additive time-varying delay components , 2016, Neurocomputing.

[11]  Dong Wang,et al.  Non‐fragile H ∞  control for switched stochastic delay systems with application to water quality process , 2014 .

[12]  Dong Wang,et al.  Cooperative Containment Control of Multiagent Systems Based on Follower Observers With Time Delay , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[13]  Hongye Su,et al.  Improved Delay-Dependent Stability Condition of Discrete Recurrent Neural Networks With Time-Varying Delays , 2010, IEEE Transactions on Neural Networks.

[14]  Rahmat A. Shoureshi,et al.  Neural networks for system identification , 1990 .

[15]  Peng Shi,et al.  Deadbeat Dissipative FIR Filtering , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Xin-Ge Liu,et al.  Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay , 2016, Neurocomputing.

[17]  Dehui Li,et al.  Less conservative stability condition for uncertain discrete-time recurrent neural networks with time-varying delays , 2016, Neurocomputing.

[18]  R. Saeks,et al.  The analysis of feedback systems , 1972 .

[19]  Ju H. Park,et al.  New criteria on delay-dependent stability for discrete-time neural networks with time-varying delays , 2013, Neurocomputing.

[20]  Yurong Liu,et al.  Passivity analysis for discrete-time neural networks with mixed time-delays and randomly occurring quantization effects , 2016, Neurocomputing.

[21]  Shouming Zhong,et al.  On extended dissipativity analysis for neural networks with time-varying delay and general activation functions , 2016 .

[22]  Zidong Wang,et al.  Global exponential stability of generalized recurrent neural networks with discrete and distributed delays , 2006, Neural Networks.

[23]  Peng Shi,et al.  Passivity and Passification for a Class of Uncertain Switched Stochastic Time-Delay Systems , 2013, IEEE Transactions on Cybernetics.

[24]  Anke Meyer-Bäse,et al.  Robust dissipativity and passivity based state estimation for discrete-time stochastic Markov jump neural networks with discrete and distributed time-varying delays , 2015, Neural Computing and Applications.

[25]  Shengyuan Xu,et al.  Filtering of Markovian Jump Delay Systems Based on a New Performance Index , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[26]  James Lam,et al.  Stability and Synchronization of Discrete-Time Neural Networks With Switching Parameters and Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[27]  Feng-Xian Wang,et al.  Asymptotical stability for a class of discrete systems with variable delay , 2015, 2015 8th International Conference on Biomedical Engineering and Informatics (BMEI).

[28]  Wei Xing Zheng,et al.  On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Qiankun Song Stochastic dissipativity analysis on discrete-time neural networks with time-varying delays , 2011, Neurocomputing.

[30]  Ju H. Park,et al.  Extended Dissipative Analysis for Neural Networks With Time-Varying Delays , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[31]  A. Arunkumar,et al.  Robust stochastic stability of discrete-time fuzzy Markovian jump neural networks. , 2014, ISA transactions.

[32]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[33]  G. Nagamani,et al.  Dissipativity and passivity analysis for discrete-time complex-valued neural networks with time-varying delay , 2015 .

[34]  K. Gopalsamy,et al.  Exponential stability of continuous-time and discrete-time cellular neural networks with delays , 2003, Appl. Math. Comput..

[35]  Pagavathigounder Balasubramaniam,et al.  Robust stability analysis for discrete-time uncertain neural networks with leakage time-varying delay , 2015, Neurocomputing.

[36]  Jun Wang,et al.  Passivity of Switched Recurrent Neural Networks With Time-Varying Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[37]  Peng Shi,et al.  Dissipativity Analysis for Discrete-Time Stochastic Neural Networks With Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[38]  Peng Shi,et al.  Generalized Dissipativity Analysis of Digital Filters With Finite-Wordlength Arithmetic , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[39]  Guanghui Sun,et al.  Dissipativity analysis for discrete-time fuzzy neural networks with leakage and time-varying delays , 2016, Neurocomputing.

[40]  Feng-Xian Wang,et al.  A novel summation inequality for stability analysis of discrete-time neural networks , 2016, J. Comput. Appl. Math..

[41]  Hao Shen,et al.  Robust extended dissipative control for sampled-data Markov jump systems , 2014, Int. J. Control.

[42]  Xiaoping Liu,et al.  Approximation-Based Adaptive Fuzzy Tracking Control for a Class of Nonstrict-Feedback Stochastic Nonlinear Time-Delay Systems , 2015, IEEE Transactions on Fuzzy Systems.

[43]  Choon Ki Ahn,et al.  Novel Results on Generalized Dissipativity of Two-Dimensional Digital Filters , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.