New Results on Passivity Analysis for Uncertain Neural Networks with Time-Varying Delay

The paper investigates the stability and passivity analysis problems for a class of uncertain neural networks with time-delay via delta operator approach. Both the parameter uncertainty and the generalized activation functions are considered in this paper. By constructing an appropriate Lyapunov-Krasovskii functional, some new stability and passivity conditions are obtained in terms of linear matrix inequalities (LMIs). The main characteristic of this paper is to obtain novel stability and passivity analysis criteria for uncertain neural networks with time-delay in the delta operator system framework. A numerical example is presented to demonstrate the effectiveness of the proposed results.

[1]  Steven X. Ding,et al.  Real-Time Implementation of Fault-Tolerant Control Systems With Performance Optimization , 2014, IEEE Transactions on Industrial Electronics.

[2]  Shaocheng Tong,et al.  Observer-Based Adaptive Fuzzy Backstepping Control for a Class of Stochastic Nonlinear Strict-Feedback Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Wei Xing Zheng,et al.  Passivity-based sliding mode control of uncertain singular time-delay systems , 2009, Autom..

[4]  Shaocheng Tong,et al.  Adaptive Fuzzy Output Feedback Tracking Backstepping Control of Strict-Feedback Nonlinear Systems With Unknown Dead Zones , 2012, IEEE Transactions on Fuzzy Systems.

[5]  Anthony N. Michel,et al.  Analysis and synthesis techniques for Hopfield type synchronous discrete time neural networks with application to associative memory , 1990 .

[6]  Z. Guan,et al.  An LMI Approach to Exponential Stability Analysis of Neural Networks with Time-Varying Delay , 2005, TENCON 2005 - 2005 IEEE Region 10 Conference.

[7]  Zhang Duan-jin.  Robust stability analysis and control for fuzzy systems with uncertainties using the delta operator , 2003 .

[8]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[9]  Jinde Cao,et al.  Global robust stability of delayed recurrent neural networks , 2004 .

[10]  Zhigang Zeng,et al.  Exponential passivity of memristive neural networks with time delays , 2014, Neural Networks.

[11]  Ping Zhang,et al.  A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process , 2012 .

[12]  X. Guan,et al.  New results on stability analysis of neural networks with time-varying delays , 2006 .

[13]  Honghai Liu,et al.  Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault , 2012, IEEE Transactions on Fuzzy Systems.

[14]  J.A. Anderson,et al.  Neural Network Models for Pattern Recognition and Associative Memory , 2002 .

[15]  Tianping Chen,et al.  Delay-independent stability analysis of Cohen-Grossberg neural networks , 2003 .

[16]  Graham C. Goodwin,et al.  Rapprochement between continuous and discrete model reference adaptive control , 1986, Autom..

[17]  Sabri Arik,et al.  An Analysis of Stability of a Class of Neutral-Type Neural Networks with Discrete Time Delays , 2013 .

[18]  Sabri Arik,et al.  Further analysis of stability of uncertain neural networks with multiple time delays , 2014 .

[19]  Sophie Keller.  Resilient Control Of Uncertain Dynamical Systems , 2016 .

[20]  Yuanqing Xia,et al.  Robust Sliding-Mode Control for Uncertain Time-Delay Systems Based on Delta Operator , 2009, IEEE Transactions on Industrial Electronics.

[21]  P. Shi,et al.  Robust adaptive sliding mode control for uncertain delta operator systems , 2009 .

[22]  S. Umar,et al.  Citrobacter rodentium‐induced NF‐κB activation in hyperproliferating colonic epithelia: role of p65 (Ser536) phosphorylation , 2006, British journal of pharmacology.

[23]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[24]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[25]  Peng Shi,et al.  Passivity Analysis for Discrete-Time Stochastic Markovian Jump Neural Networks With Mixed Time Delays , 2011, IEEE Transactions on Neural Networks.

[26]  Peng Shi,et al.  Fault-Tolerant Control for Nonlinear Markovian Jump Systems via Proportional and Derivative Sliding Mode Observer Technique , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  H. Karimi,et al.  Finite-time l1-gain control for positive switched systems with time-varying delay via delta operator approach , 2014 .

[28]  J. Lam,et al.  Delay-dependent exponential stability for a class of neural networks with time delays , 2005 .

[29]  Chun-Guang Li,et al.  Passivity Analysis of Neural Networks With Time Delay , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[30]  Huijun Gao,et al.  New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays , 2010, Neurocomputing.

[31]  Gail A. Carpenter,et al.  Neural network models for pattern recognition and associative memory , 1989, Neural Networks.

[32]  Shengyuan Xu,et al.  Passivity Analysis of Neural Networks With Time-Varying Delays , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[33]  Huijun Gao,et al.  A New Model Transformation of Discrete-Time Systems With Time-Varying Delay and Its Application to Stability Analysis , 2011, IEEE Transactions on Automatic Control.

[34]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[35]  O. Kaynak,et al.  Asymptotic stability and stabilisation of uncertain delta operator systems with time-varying delays , 2013 .

[36]  E. Jury,et al.  On Robust Stability of Discrete-Time Systems using Delta-Operators , 1992, 1992 American Control Conference.

[37]  Hayakawa,et al.  Effects of the chaotic noise on the performance of a neural network model for optimization problems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[38]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[39]  Sabri Arik,et al.  An analysis of global asymptotic stability of delayed cellular neural networks , 2002, IEEE Trans. Neural Networks.

[40]  Shengyuan Xu,et al.  A new approach to exponential stability analysis of neural networks with time-varying delays , 2006, Neural Networks.

[41]  Qiankun Song,et al.  Passivity analysis of discrete-time stochastic neural networks with time-varying delays , 2009, Neurocomputing.

[42]  Huijun Gao,et al.  ${H}_{\infty }$ Filtering for Discrete-Time State-Delayed Systems With Finite Frequency Specifications , 2011, IEEE Transactions on Automatic Control.

[43]  Huijun Gao,et al.  New Passivity Analysis for Neural Networks With Discrete and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[44]  J. Qiu,et al.  Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators , 2008 .

[45]  Jianbin Qiu,et al.  A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay , 2009, IEEE Transactions on Fuzzy Systems.

[46]  李永明,et al.  Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on small-gain approach , 2014 .

[47]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

[48]  Carsten Peterson,et al.  A New Method for Mapping Optimization Problems Onto Neural Networks , 1989, Int. J. Neural Syst..

[49]  Herbert Witte,et al.  Common Optimization of Adaptive Preprocessing Units and a Neural Network during the Learning Period. Application in EEG Pattern Recognition , 1997, Neural Networks.

[50]  Maozhen Li,et al.  Stability analysis for stochastic Cohen-Grossberg neural networks with mixed time delays , 2006, IEEE Transactions on Neural Networks.

[51]  Ju H. Park,et al.  Passivity-based control for Hopfield neural networks using convex representation , 2011, Appl. Math. Comput..

[52]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[53]  C. B. Soh,et al.  Robust stability of discrete-time systems using delta operators , 1991 .

[54]  Jianbin Qiu,et al.  Improved Delay-Dependent $H_{\infty }$ Filtering Design for Discrete-Time Polytopic Linear Delay Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[55]  Hamid Reza Karimi,et al.  Output-Feedback-Based $H_{\infty}$ Control for Vehicle Suspension Systems With Control Delay , 2014, IEEE Transactions on Industrial Electronics.

[56]  Xiefu Jiang,et al.  Stability criteria for linear discrete-time systems with interval-like time-varying delay , 2005, Proceedings of the 2005, American Control Conference, 2005..