State estimation of T-S fuzzy delayed neural networks with Markovian jumping parameters using sampled-data control

Abstract In this paper, we are concerned with the problem of state estimation of Takagi–Sugeno (T–S) fuzzy delayed neural networks with Markovian jumping parameters via sampled-data control. Based on the fuzzy-model-based control approach and linear matrix inequality (LMI) technique, several novel conditions are derived to guarantee the stability of the suggested system. A new class of Lyapunov functional, which contains integral terms, is constructed to derive delay-dependent stability criteria. Some characteristics of the sampling input delay are proposed based on the input delay approach. Numerical examples are given to illustrate the usefulness and effectiveness of the proposed theoretical results.

[1]  Engang Tian,et al.  Delay-dependent stability analysis and synthesis of uncertain T-S fuzzy systems with time-varying delay , 2006, Fuzzy Sets Syst..

[2]  Jian Sun,et al.  Improved stability criteria for neural networks with time-varying delay , 2009 .

[3]  Yongming Li,et al.  Observer-Based Adaptive Fuzzy Backstepping Dynamic Surface Control for a Class of MIMO Nonlinear Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[4]  Ju H. Park,et al.  Exponential synchronization criteria for Markovian jumping neural networks with time-varying delays and sampled-data control , 2014 .

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

[6]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[7]  Jinde Cao,et al.  Switched exponential state estimation and robust stability for interval neural networks with the average dwell time , 2015, IMA J. Math. Control. Inf..

[8]  D. Ho,et al.  Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay , 2007 .

[9]  Tae H. Lee,et al.  Stochastic sampled-data control for state estimation of time-varying delayed neural networks , 2013, Neural Networks.

[10]  Yong He,et al.  Complete Delay-Decomposing Approach to Asymptotic Stability for Neural Networks With Time-Varying Delays , 2011, IEEE Transactions on Neural Networks.

[11]  Guilin Wen,et al.  Improved stability criteria for time-varying delayed T-S fuzzy systems via delay partitioning approach , 2011, Fuzzy Sets Syst..

[12]  Shaocheng Tong,et al.  Fuzzy Adaptive Output Feedback Control of MIMO Nonlinear Systems With Partial Tracking Errors Constrained , 2015, IEEE Transactions on Fuzzy Systems.

[13]  Jinde Cao,et al.  Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay , 2011, Neural Networks.

[14]  Shaocheng Tong,et al.  Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay , 2006, Fuzzy Sets Syst..

[15]  Nan Li,et al.  Sampled-data state estimation for delayed neural networks with Markovian jumping parameters , 2013 .

[16]  M. Syed Ali,et al.  Stochastic stability of discrete-time uncertain recurrent neural networks with Markovian jumping and time-varying delays , 2011, Math. Comput. Model..

[17]  Pagavathigounder Balasubramaniam,et al.  Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple time-varying delays , 2010, Expert Syst. Appl..

[18]  Kazuo Tanaka,et al.  Stability analysis and design of fuzzy control systems , 1992 .

[19]  Ju H. Park,et al.  Sampled-data state estimation for Markovian jumping fuzzy cellular neural networks with mode-dependent probabilistic time-varying delays , 2013, Appl. Math. Comput..

[20]  Pin-Lin Liu.  Improved delay-dependent robust stability criteria for recurrent neural networks with time-varying delays. , 2013, ISA transactions.

[21]  Daniel W. C. Ho,et al.  State estimation for delayed neural networks , 2005, IEEE Transactions on Neural Networks.

[22]  Xin-Ping Guan,et al.  New Delay-Dependent Stability Criteria for Neural Networks With Time-Varying Delay Using Delay-Decomposition Approach , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[23]  M. Syed Ali,et al.  Novel delay-dependent stability analysis of Takagi—Sugeno fuzzy uncertain neural networks with time varying delays , 2012 .

[24]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[25]  Huijun Gao,et al.  Network-Induced Constraints in Networked Control Systems—A Survey , 2013, IEEE Transactions on Industrial Informatics.

[26]  Pagavathigounder Balasubramaniam,et al.  Delay-dependent robust asymptotic state estimation of Takagi-Sugeno fuzzy Hopfield neural networks with mixed interval time-varying delays , 2012, Expert Syst. Appl..

[27]  M. Syed Ali,et al.  Stability analysis of Takagi-Sugeno stochastic fuzzy Hopfield neural networks with discrete and distributed time varying delays , 2011, Neurocomputing.

[28]  Shengyuan Xu,et al.  Delay-dependent H∞ filtering for stochastic systems with Markovian switching and mixed mode-dependent delays , 2010 .

[29]  Jinde Cao,et al.  Guaranteed performance state estimation of static neural networks with time-varying delay , 2011, Neurocomputing.

[30]  Pin-Lin Liu,et al.  Robust exponential stability for uncertain time-varying delay systems with delay dependence , 2009, J. Frankl. Inst..

[31]  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).

[32]  Jun Hu,et al.  Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters , 2010, Neural Networks.

[33]  Fang Xu,et al.  Improved delay-partitioning method to stability analysis for neural networks with discrete and distributed time-varying delays , 2014, Appl. Math. Comput..

[34]  P. Balasubramaniam,et al.  State estimation for Markovian jumping recurrent neural networks with interval time-varying delays , 2010 .

[35]  Shouming Zhong,et al.  Improved delay-dependent stability criterion for neural networks with time-varying delay , 2011, Appl. Math. Comput..

[36]  Qiankun Song,et al.  Exponential stability of recurrent neural networks with both time-varying delays and general activation functions via LMI approach , 2008, Neurocomputing.

[37]  Shaocheng Tong,et al.  A Combined Backstepping and Stochastic Small-Gain Approach to Robust Adaptive Fuzzy Output Feedback Control , 2013, IEEE Transactions on Fuzzy Systems.

[38]  B. Chen,et al.  Delay-Dependent Robust H∞ Control for T-S Fuzzy Systems With Time Delay , 2005, IEEE Trans. Fuzzy Syst..

[39]  R. Rakkiyappan,et al.  Design of sampled data state estimator for Markovian jumping neural networks with leakage time-varying delays and discontinuous Lyapunov functional approach , 2013 .

[40]  Youyi Wang,et al.  Stabilization for Sampled-Data Neural-Network-Based Control Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[41]  Xuerong Mao,et al.  Stochastic differential equations and their applications , 1997 .

[42]  Ju H. Park,et al.  State estimation of neural networks with time-varying delays and Markovian jumping parameter based on passivity theory , 2012 .

[43]  Pagavathigounder Balasubramaniam,et al.  Stability analysis of Takagi-Sugeno fuzzy Cohen-Grossberg BAM neural networks with discrete and distributed time-varying delays , 2011, Math. Comput. Model..

[44]  Huijun Gao,et al.  Robust sampled-data H∞ control with stochastic sampling , 2009, Autom..

[45]  Shouming Zhong,et al.  Improved delay-dependent stability criteria for recurrent neural networks with time-varying delays , 2014, Neurocomputing.

[46]  Xiaodong Liu,et al.  Stability analysis for neural networks with time-varying delay , 2008, 2008 47th IEEE Conference on Decision and Control.

[47]  Huijun Gao,et al.  Robust Sampled-Data $H_{\infty}$ Control for Vehicle Active Suspension Systems , 2010, IEEE Transactions on Control Systems Technology.

[48]  Wei Xing Zheng,et al.  Delay-Slope-Dependent Stability Results of Recurrent Neural Networks , 2011, IEEE Transactions on Neural Networks.

[49]  Gang Feng,et al.  State estimation of recurrent neural networks with time-varying delay: A novel delay partition approach , 2011, Neurocomputing.

[50]  Farid Sheikholeslam,et al.  Stability analysis and design of fuzzy control systems , 1998, 1998 IEEE International Conference on Fuzzy Systems Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36228).

[51]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[52]  Ju H. Park,et al.  Further results on state estimation for neural networks of neutral-type with time-varying delay , 2009, Appl. Math. Comput..

[54]  Jinde Cao,et al.  An LMI approach to delay-dependent state estimation for delayed neural networks , 2008, Neurocomputing.

[55]  Shouming Zhong,et al.  State estimation for neural networks with multiple time delays , 2015, Neurocomputing.

[56]  Sabri Arik,et al.  An improved robust stability result for uncertain neural networks with multiple time delays , 2014, Neural Networks.