Delay-dependent dissipativity criteria for Markovian jump neural networks with random delays and incomplete transition probabilities

2018 ◽  
Vol 91 (4) ◽  
pp. 2503-2522 ◽  
Author(s):  
G. Nagamani ◽  
Young Hoon Joo ◽  
T. Radhika
Keyword(s):  
Neural Networks ◽  
Transition Probabilities ◽  
Markovian Jump ◽  
Random Delays ◽  
Delay Dependent ◽  
Markovian Jump Neural Networks

scholarly journals Finite-Time H ∞ State Estimation for Markovian Jump Neural Networks with Time-Varying Delays via an Extended Wirtinger’s Integral Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Saravanan Shanmugam ◽  
M. Syed Ali ◽  
R. Vadivel ◽  
Gyu M. Lee
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jumping ◽  
Double Inequality ◽  
Markovian Jump Neural Networks

This study investigates the finite-time boundedness for Markovian jump neural networks (MJNNs) with time-varying delays. An MJNN consists of a limited number of jumping modes wherein it can jump starting with one mode then onto the next by following a Markovian process with known transition probabilities. By constructing new Lyapunov–Krasovskii functional (LKF) candidates, extended Wirtinger’s, and Wirtinger’s double inequality with multiple integral terms and using activation function conditions, several sufficient conditions for Markovian jumping neural networks are derived. Furthermore, delay-dependent adequate conditions on guaranteeing the closed-loop system which are stochastically finite-time bounded (SFTB) with the prescribed H ∞ performance level are proposed. Linear matrix inequalities are utilized to obtain analysis results. The purpose is to obtain less conservative conditions on finite-time H ∞ performance for Markovian jump neural networks with time-varying delay. Eventually, simulation examples are provided to illustrate the validity of the addressed method.

scholarly journals Stability Analysis of Stochastic Markovian Jump Neural Networks with Different Time Scales and Randomly Occurred Nonlinearities Based on Delay-Partitioning Projection Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Jianmin Duan ◽  
Manfeng Hu ◽  
Yongqing Yang ◽  
Liuxiao Guo
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Linear Matrix ◽  
Markovian Jump ◽  
Projection Approach ◽  
Delay Dependent ◽  
Delay Partitioning ◽  
Delay Dependent Stability ◽  
Different Time Scales ◽  
Markovian Jump Neural Networks

In this paper, the mean square asymptotic stability of stochastic Markovian jump neural networks with different time scales and randomly occurred nonlinearities is investigated. In terms of linear matrix inequality (LMI) approach and delay-partitioning projection technique, delay-dependent stability criteria are derived for the considered neural networks for cases with or without the information of the delay rates via new Lyapunov-Krasovskii functionals. We also obtain that the thinner the delay is partitioned, the more obviously the conservatism can be reduced. An example with simulation results is given to show the effectiveness of the proposed approach.

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