Non-fragile L 2 − L ∞ synchronization for chaotic time-delay neural networks with semi-Markovian jump parameters

The issue of the non-fragile L 2 − L ∞ synchronization for chaotic time-delay neural networks subject to semi-Markovian jump parameters is addressed in this paper. Unlike the Markovian jump process, the sojourn time of the semi-Markovian jump process allows to be non-exponential distributed and the transition rate allows to be time-varying. By utilizing the discretized Lyapunov–Krasovskii functional method and introducing two free-weighting matrices, a sufficient condition is proposed to ensure the synchronization error system to be stochastically stable with an L 2 − L ∞ performance index. Then, by means of a matrix congruence transformation and some inequality techniques, an approach to the non-fragile L 2 − L ∞ controller design is developed. Finally, two illustrative examples are employed to show the usefulness of the proposed results.

[1]  Jinde Cao,et al.  Input-to-State Stability of Time-Varying Switched Systems With Time Delays , 2019, IEEE Transactions on Automatic Control.

[2]  Jinde Cao,et al.  Stability Analysis for Continuous-Time Switched Systems With Stochastic Switching Signals , 2018, IEEE Transactions on Automatic Control.

[3]  Jianping Zhou,et al.  Energy-to-peak consensus for multi-agent systems with stochastic disturbances and Markovian switching topologies , 2018, Trans. Inst. Meas. Control.

[4]  Chaoxu Guan,et al.  Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Choon Ki Ahn,et al.  L 2 - L ∞ filtering for time-delayed switched hopfield neural networks , 2011 .

[6]  Yongcan Cao,et al.  Exponential l2−l∞ output tracking control for discrete‐time switched system with time‐varying delay , 2012 .

[7]  X. Mao.  Stability of stochastic differential equations with Markovian switching , 1999 .

[8]  Jinde Cao,et al.  Nonfragile Dissipative Synchronization for Markovian Memristive Neural Networks: A Gain-Scheduled Control Scheme , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[9]  Chee Peng Lim,et al.  Observer-Based $\mathcal{H}_{\infty }$ Fault-Tolerant Control for Linear Systems With Sensor and Actuator Faults , 2019, IEEE Systems Journal.

[10]  M. Manhart,et al.  Markov Processes , 2018, Introduction to Stochastic Processes and Simulation.

[11]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[12]  Jinde Cao,et al.  Finite-time boundedness, L2-gain analysis and control of Markovian jump switched neural networks with additive time-varying delays , 2017 .

[13]  Jinde Cao,et al.  Robust fixed-time synchronization for uncertain complex-valued neural networks with discontinuous activation functions , 2017, Neural Networks.

[14]  Yoshua Bengio,et al.  The problem of learning long-term dependencies in recurrent networks , 1993, IEEE International Conference on Neural Networks.

[15]  Jianwei Xia,et al.  Aperiodically Intermittent Control for Quasi-Synchronization of Delayed Memristive Neural Networks: An Interval Matrix and Matrix Measure Combined Method , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[16]  Jianwei Xia,et al.  Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks , 2018, Advances in Difference Equations.

[17]  Jun Wang,et al.  Reliable asynchronous sampled-data filtering of T-S fuzzy uncertain delayed neural networks with stochastic switched topologies , 2020, Fuzzy Sets Syst..

[18]  Funa Zhou,et al.  Event‐triggered dissipative synchronization for Markovian jump neural networks with general transition probabilities , 2018 .

[19]  Hamid Reza Karimi,et al.  Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[20]  Ian R. Petersen,et al.  A riccati equation approach to the stabilization of uncertain linear systems , 1986, Autom..

[21]  Shengyuan Xu,et al.  Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays , 2019, Appl. Math. Comput..

[22]  Linshan Wang,et al.  Robust Exponential Synchronization for Stochastic Delayed Neural Networks with Reaction–Diffusion Terms and Markovian Jumping Parameters , 2018, Neural Processing Letters.

[23]  Hamid Reza Karimi,et al.  New Criteria for Stability of Generalized Neural Networks Including Markov Jump Parameters and Additive Time Delays , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Yang Wang,et al.  Weighted $${\mathcal {H}}_{\infty }$$H∞ consensus design for stochastic multi-agent systems subject to external disturbances and ADT switching topologies , 2019, Nonlinear Dynamics.

[25]  Sabri Arik,et al.  New Criteria for Stability of Neutral-Type Neural Networks With Multiple Time Delays , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[26]  Yunliang Wei,et al.  Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays , 2018, Appl. Math. Comput..

[27]  R. Sakthivel,et al.  New exponential stability criteria for stochastic BAM neural networks with impulses , 2010 .

[28]  Qian Ma,et al.  Non-fragile observer-based H∞ control for stochastic time-delay systems , 2016, Appl. Math. Comput..

[29]  Zhen Wang,et al.  Consensus for Nonlinear Stochastic Multi-agent Systems with Time Delay , 2018, Appl. Math. Comput..

[30]  Hui Gao,et al.  Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems , 2018, J. Frankl. Inst..

[31]  Pagavathigounder Balasubramaniam,et al.  Non-fragile observer design for discrete-time genetic regulatory networks with randomly occurring uncertainties , 2014 .

[32]  Jianping Zhou,et al.  Chaos synchronization of stochastic reaction-diffusion time-delay neural networks via non-fragile output-feedback control , 2019, Appl. Math. Comput..

[33]  Dimitrios Zissis,et al.  A cloud based architecture capable of perceiving and predicting multiple vessel behaviour , 2015, Appl. Soft Comput..

[34]  Jianwei Xia,et al.  Extended dissipative learning of time-delay recurrent neural networks , 2019, J. Frankl. Inst..

[35]  Yang Cao,et al.  An event-triggered synchronization of semi-Markov jump neural networks with time-varying delays based on generalized free-weighting-matrix approach , 2017, Math. Comput. Simul..

[36]  Jinde Cao,et al.  Global dissipativity analysis on uncertain neural networks with mixed time-varying delays. , 2008, Chaos.

[37]  Goutam Saha,et al.  Lung sound classification using cepstral-based statistical features , 2016, Comput. Biol. Medicine.

[38]  Muyun 木云 Fang 方,et al.  ℋ∞ couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies , 2019 .

[39]  Yang Shi,et al.  Stochastic stability and robust stabilization of semi‐Markov jump linear systems , 2013 .

[40]  Gang Feng,et al.  Synchronization of nonidentical chaotic neural networks with time delays , 2009, Neural Networks.

[41]  Yang Wang,et al.  Weighted H ∞ consensus design for stochastic multi-agent systems subject to external disturbances and ADT switching topologies. , 2019 .

[42]  Xiaohui Hu,et al.  Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays , 2019, Appl. Math. Comput..

[43]  Lingfeng Liu,et al.  Cluster synchronization in a complex dynamical network of non-identical nodes with delayed and non-delayed coupling via pinning control , 2019, Physica Scripta.

[44]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[45]  Chai Wah Wu,et al.  A Simple Way to Synchronize Chaotic Systems with Applications to , 1993 .

[46]  Le-Pond Chin,et al.  Application of neural networks in target tracking data fusion , 1994 .

[47]  Guang-Hong Yang,et al.  Nonfragile $H_{\infty}$ Filter Design for T–S Fuzzy Systems in Standard Form , 2014, IEEE Transactions on Industrial Electronics.

[48]  Xiao Li,et al.  ${ {\mathcal H} }_{\infty }$ couple-group consensus of stochastic multi-agent systems with fixed and Markovian switching communication topologies , 2019, Chinese Physics B.

[49]  Xiao-Heng Chang,et al.  A Further Study on Output Feedback $\mathcal{H}_{\infty}$ Control for Discrete-Time Systems , 2020, IEEE Transactions on Circuits and Systems II: Express Briefs.

[50]  Rathinasamy Sakthivel,et al.  Robust reliable L2 - L∞ control for continuous-time systems with nonlinear actuator failures , 2016, Complex..

[51]  Jie Tan,et al.  Decentralized Finite-time L2-L∞ tracking control for a class of interconnected Markovian jump system with actuator saturation. , 2019, ISA transactions.