H∞ Synchronization of Semi-Markovian Jump Neural Networks with Randomly Occurring Time-Varying Delays

Based on the Lyapunov stability theory, this paper mainly investigates the H∞ synchronization problem for semi-Markovian jump neural networks (semi-MJNNs) with randomly occurring time-varying delays (TVDs). The continuous-time semi-MJNNs, where the transition rates are dependent on sojourn time, are introduced to make the issue under our consideration more general. One of the main characteristics of our work is the handling of TVDs. In addition to using the improved Jensen inequality and the reciprocal convexity lemma to deal with the integral inequality, we also employ Schur complement and the projection lemma to achieve the decoupling between the square term of TVDs. Finally, we verify the validity and feasibility of our method by a couple of simulation examples.

Download Full-text

Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay

IEEE Transactions on Neural Networks and Learning Systems ◽

10.1109/tnnls.2017.2696582 ◽

2018 ◽

Vol 29 (6) ◽

pp. 2488-2501 ◽

Cited By ~ 102

Author(s):

Yanling Wei ◽

Ju H. Park ◽

Hamid Reza Karimi ◽

Yu-Chu Tian ◽

Hoyoul Jung

Keyword(s):

Neural Networks ◽

Continuous Time ◽

Time Varying ◽

Markovian Jump ◽

Stochastic Synchronization ◽

Time Varying Delay ◽

Improved Stability ◽

Stability And Stabilization ◽

Varying Delay ◽

Markovian Jump Neural Networks

Download Full-text

Finite-time sampled-data synchronization for uncertain neutral-type semi-Markovian jump neural networks with mixed time-varying delays

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126197 ◽

2021 ◽

Vol 403 ◽

pp. 126197

Author(s):

Yao Wang ◽

Jun Guo ◽

Guobao Liu ◽

Junwei Lu ◽

Fangyuan Li

Keyword(s):

Neural Networks ◽

Finite Time ◽

Neutral Type ◽

Data Synchronization ◽

Time Varying ◽

Sampled Data ◽

Markovian Jump ◽

Markovian Jump Neural Networks

Download Full-text

Dissipativity Analysis for Markovian Jump Neural Networks with Time-Varying Delay via An Extended Relaxed Integral Inequality

2018 37th Chinese Control Conference (CCC) ◽

10.23919/chicc.2018.8483888 ◽

2018 ◽

Author(s):

LIN Wen-Juan ◽

HE Yong

Keyword(s):

Neural Networks ◽

Integral Inequality ◽

Time Varying ◽

Markovian Jump ◽

Time Varying Delay ◽

Dissipativity Analysis ◽

Varying Delay ◽

Markovian Jump Neural Networks

Download Full-text

Reachable set estimation for Markovian jump neural networks with time-varying delay

Neural Networks ◽

10.1016/j.neunet.2018.09.011 ◽

2018 ◽

Vol 108 ◽

pp. 527-532 ◽

Cited By ~ 15

Author(s):

Wen-Juan Lin ◽

Yong He ◽

Min Wu ◽

Qingping Liu

Keyword(s):

Neural Networks ◽

Reachable Set ◽

Time Varying ◽

Markovian Jump ◽

Time Varying Delay ◽

Set Estimation ◽

Reachable Set Estimation ◽

Varying Delay ◽

Markovian Jump Neural Networks

Download Full-text

Finite-Horizon $l_2-l_\infty$ Synchronization for Time-Varying Markovian Jump Neural Networks Under Mixed-Type Attacks: Observer-Based Case

IEEE Transactions on Neural Networks and Learning Systems ◽

10.1109/tnnls.2018.2873163 ◽

2019 ◽

Vol 30 (6) ◽

pp. 1695-1704 ◽

Cited By ~ 18

Author(s):

Yong Xu ◽

Jun-Yi Li ◽

Renquan Lu ◽

Chang Liu ◽

Yuanqing Wu

Keyword(s):

Neural Networks ◽

Mixed Type ◽

Finite Horizon ◽

Time Varying ◽

Markovian Jump ◽

Markovian Jump Neural Networks

Download Full-text

Stability criteria for Markovian jump neural networks with mode-dependent additive time-varying delays via quadratic convex combination

Neurocomputing ◽

10.1016/j.neucom.2016.03.058 ◽

2016 ◽

Vol 205 ◽

pp. 75-83 ◽

Cited By ~ 25

Author(s):

P. Muthukumar ◽

K. Subramanian

Keyword(s):

Neural Networks ◽

Convex Combination ◽

Time Varying ◽

Stability Criteria ◽

Markovian Jump ◽

Markovian Jump Neural Networks

Download Full-text

Stochastic Finite-Time H∞ State Estimation for Discrete-Time Semi-Markovian Jump Neural Networks With Time-Varying Delays

IEEE Transactions on Neural Networks and Learning Systems ◽

10.1109/tnnls.2020.2968074 ◽

2020 ◽

Vol 31 (12) ◽

pp. 5456-5467 ◽

Cited By ~ 3

Author(s):

Wen-Juan Lin ◽

Yong He ◽

Chuan-Ke Zhang ◽

Min Wu

Keyword(s):

Neural Networks ◽

State Estimation ◽

Discrete Time ◽

Finite Time ◽

Time Varying ◽

Markovian Jump ◽

Markovian Jump Neural Networks

Download Full-text

Aperiodic Sampled-data Controller Design of Stochastic Markovian Jump Neural Networks With Time-Varying Delay

2020 International Conference on System Science and Engineering (ICSSE) ◽

10.1109/icsse50014.2020.9219299 ◽

2020 ◽

Author(s):

Guoliang Chen ◽

Te Yang ◽

Jianwei Xia

Keyword(s):

Neural Networks ◽

Controller Design ◽

Time Varying ◽

Sampled Data ◽

Markovian Jump ◽

Time Varying Delay ◽

Data Controller ◽

Varying Delay ◽

Markovian Jump Neural Networks

Download Full-text

On Exponential Stability for a Class of Uncertain Neutral Markovian Jump Systems with Mode-Dependent Delays

Abstract and Applied Analysis ◽

10.1155/2013/691650 ◽

2013 ◽

Vol 2013 ◽

pp. 1-23

Author(s):

Xinghua Liu ◽

Hongsheng Xi

Keyword(s):

Exponential Stability ◽

Lyapunov Stability Theory ◽

Markovian Jump Systems ◽

Time Varying ◽

Transition Rates ◽

Stability Criteria ◽

Markovian Jump ◽

Rate Dependent ◽

Partially Known Transition Rates ◽

Jump Systems

The exponential stability of neutral Markovian jump systems with interval mode-dependent time-varying delays, nonlinear perturbations, and partially known transition rates is investigated. A novel augmented stochastic Lyapunov functional is constructed, which employs the improved bounding technique and contains triple-integral terms to reduce conservativeness; then the delay-range-dependent and rate-dependent exponential stability criteria are developed by Lyapunov stability theory, reciprocally convex lemma, and free-weighting matrices. The corresponding results are extended to the uncertain case. Finally, numerical examples are given to illustrate the effectiveness of the proposed methods.

Download Full-text