Stochastic Exponential Stabilization for Markov Jump Neural Networks with Time-varying Delays via Adaptive Event-Triggered Impulsive Control

This paper focuses on the exponential stabilization problem for Markov jump neural networks with Time-varying Delays (TDs). Firstly, we provide a new Free-matrix-based Exponential-type Integral Inequality (FMEII) containing the information of attenuation exponent, which is helpful to reduce the conservativeness of stability criteria. To further save control cost, we introduce a sample-based Adaptive Event-triggered Impulsive Control (AEIC) scheme, in which the trigger threshold is adaptively varied with the sampled state. By fully considering the information about sampled state, TDs, and Markov jump parameters, a suitable Lyapunov–Krasovskii functional is constructed. With the virtue of FMEII and AEIC scheme, some novel stabilization criteria are presented in the form of linear matrix inequalities. At last, two numerical examples are given to show the validity of the obtained results.

[1]  Hieu Minh Trinh,et al.  Exponential stability of time-delay systems via new weighted integral inequalities , 2015, Appl. Math. Comput..

[2]  Wei Xing Zheng,et al.  Distributed ℋ∞ Filtering for a Class of Discrete-Time Markov Jump Lur'e Systems With Redundant Channels , 2016, IEEE Trans. Ind. Electron..

[3]  Liqun Zhou,et al.  Delay-dependent exponential stability of recurrent neural networks with Markovian jumping parameters and proportional delays , 2016, Neural Computing and Applications.

[4]  Jinde Cao,et al.  An Event-Based Asynchronous Approach to Markov Jump Systems With Hidden Mode Detections and Missing Measurements , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[5]  Sreten B. Stojanovic,et al.  Finite-Time Passivity-Based Stability Criteria for Delayed Discrete-Time Neural Networks via New Weighted Summation Inequalities , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[6]  PooGyeon Park,et al.  Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems , 2015, J. Frankl. Inst..

[7]  Jinde Cao,et al.  Exponential stability and extended dissipativity criteria for generalized neural networks with interval time-varying delay signals , 2017, J. Frankl. Inst..

[8]  Yunlong Liu,et al.  Exponential Stability of Neutral-Type Impulsive Markovian Jump Neural Networks with General Incomplete Transition Rates , 2017, Neural Processing Letters.

[9]  Young Hoon Joo,et al.  Exponential dissipativity criteria for generalized BAM neural networks with variable delays , 2017, Neural Computing and Applications.

[10]  Zhigang Zeng,et al.  Circuit design and exponential stabilization of memristive neural networks , 2015, Neural Networks.

[11]  Jinde Cao,et al.  Consensus of Leader-Following Multiagent Systems: A Distributed Event-Triggered Impulsive Control Strategy , 2019, IEEE Transactions on Cybernetics.

[12]  Yong He,et al.  Global exponential stability of neural networks with time-varying delay based on free-matrix-based integral inequality , 2016, Neural Networks.

[13]  R. Rakkiyappan,et al.  Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control , 2014, Neurocomputing.

[14]  Changyin Sun,et al.  Exponential stability of recurrent neural networks with time-varying discrete and distributed delays , 2009 .

[15]  Gang Feng,et al.  Event-Based Impulsive Control of Continuous-Time Dynamic Systems and Its Application to Synchronization of Memristive Neural Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[16]  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.

[17]  Seakweng Vong,et al.  Improved exponential stability criteria of time-delay systems via weighted integral inequalities , 2018, Appl. Math. Lett..

[18]  Xin Zhang,et al.  Exponential Stability of Neural Networks with Markovian Switching Parameters and General Noise , 2019 .

[19]  Shiji Song,et al.  Input-to-State Stability of Nonlinear Systems Using Observer-Based Event-Triggered Impulsive Control , 2020, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[20]  Peng Shi,et al.  Event‐based dissipative analysis for discrete time‐delay singular stochastic systems , 2018, International Journal of Robust and Nonlinear Control.

[21]  Huaguang Zhang,et al.  Sampled-Data Synchronization Analysis of Markovian Neural Networks With Generally Incomplete Transition Rates , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[22]  Victor Sreeram,et al.  Fuzzy-Model-Based Nonfragile Control for Nonlinear Singularly Perturbed Systems With Semi-Markov Jump Parameters , 2018, IEEE Transactions on Fuzzy Systems.

[23]  Jeng-Shyang Pan,et al.  Finite-time boundedness of Markovain jump nonlinear systems with incomplete information , 2018, Int. J. Syst. Sci..

[24]  Bin Liu,et al.  Stabilisation to input‐to‐state stability for continuous‐time dynamical systems via event‐triggered impulsive control with three levels of events , 2018, IET Control Theory & Applications.

[25]  M. Syed Ali,et al.  Event-triggered state estimation for Markovian jumping impulsive neural networks with interval time-varying delays , 2019, Int. J. Control.

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

[27]  Chen Peng,et al.  A survey on recent advances in event-triggered communication and control , 2018, Inf. Sci..

[28]  Ju H. Park,et al.  Global Exponential Stability of Delayed Neural Networks Based on a New Integral Inequality , 2019, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[29]  Sing Kiong Nguang,et al.  Stability Analysis of Genetic Regulatory Networks With General Random Disturbances , 2019, IEEE Transactions on NanoBioscience.

[30]  S. C. Shrivastava,et al.  Neural network applications in smart antenna arrays: A review , 2012 .

[31]  Menglong Cao,et al.  Input-to-State Stabilization of Nonlinear Systems via Event-Triggered Impulsive Control , 2019, IEEE Access.

[32]  Zhenjiang Zhao,et al.  Passivity analysis of stochastic neural networks with time-varying delays and leakage delay , 2014, Neurocomputing.

[33]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[34]  Zhigang Zeng,et al.  Event-triggered impulsive control on quasi-synchronization of memristive neural networks with time-varying delays , 2019, Neural Networks.

[35]  Jinde Cao,et al.  Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters , 2009 .