scholarly journals Passivity Analysis of Markovian Jumping Neural Networks with Leakage Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
N. Mala ◽  
A. R. Sudamani Ramaswamy
Keyword(s):  
Neural Networks ◽  
Upper Bound ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Time Varying ◽  
Markovian Jumping ◽  
Mixed Time Delays ◽  
Passivity Analysis ◽  
Delay Dependent

This paper is concerned with the passivity analysis of Markovian jumping neural networks with leakage time-varying delays. Based on a Lyapunov functional that accounts for the mixed time delays, a leakage delay-dependent passivity conditions are derived in terms of linear matrix inequalities (LMIs). The mixed delays includes leakage time-varying delays, discrete time-varying delays, and distributed time-varying delays. By employing a novel Lyapunov-Krasovskii functional having triple-integral terms, new passivity leakage delay-dependent criteria are established to guarantee the passivity performance. This performance not only depends on the upper bound of the time-varying leakage delay but also depends on the upper bound of the derivative of the time-varying leakage delay . While estimating the upper bound of derivative of the Lyapunov-Krasovskii functional, the discrete and distributed delays should be treated so as to appropriately develop less conservative results. Two numerical examples are given to show the validity and potential of the developed criteria.

Robust Stochastic Stability of Discrete-Time Markovian Jump Neural Networks with Leakage Delay

2014 ◽  
Vol 69 (1-2) ◽  
pp. 70-80 ◽  
Author(s):  
Mathiyalagan Kalidass ◽  
Hongye Su ◽  
Sakthivel Rathinasamy
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Stochastic Stability ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Weighting Matrix ◽  
The Stability ◽  
Delay Dependent

This paper presents a robust analysis approach to stochastic stability of the uncertain Markovian jumping discrete-time neural networks (MJDNNs) with time delay in the leakage term. By choosing an appropriate Lyapunov functional and using free weighting matrix technique, a set of delay dependent stability criteria are derived. The stability results are delay dependent, which depend on not only the upper bounds of time delays but also their lower bounds. The obtained stability criteria are established in terms of linear matrix inequalities (LMIs) which can be effectively solved by some standard numerical packages. Finally, some illustrative numerical examples with simulation results are provided to demonstrate applicability of the obtained results. It is shown that even if there is no leakage delay, the obtained results are less restrictive than in some recent works.

Synchronization of Uncertain Neural Networks with H8 Performance and Mixed Time-Delays

2011 ◽  
pp. 1208-1232
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

scholarly journals Globalμ-Stability of Impulsive Complex-Valued Neural Networks with Leakage Delay and Mixed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaofeng Chen ◽  
Qiankun Song ◽  
Yurong Liu ◽  
Zhenjiang Zhao
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Distributed Delay ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Weighting Matrix ◽  
Homeomorphism Mapping ◽  
Delay Dependent ◽  
Complex Valued

The impulsive complex-valued neural networks with three kinds of time delays including leakage delay, discrete delay, and distributed delay are considered. Based on the homeomorphism mapping principle of complex domain, a sufficient condition for the existence and uniqueness of the equilibrium point of the addressed complex-valued neural networks is proposed in terms of linear matrix inequality (LMI). By constructing appropriate Lyapunov-Krasovskii functionals, and employing the free weighting matrix method, several delay-dependent criteria for checking the globalμ-stability of the complex-valued neural networks are established in LMIs. As direct applications of these results, several criteria on the exponential stability, power-stability, and log-stability are obtained. Two examples with simulations are provided to demonstrate the effectiveness of the proposed criteria.

scholarly journals New Results on Passivity for Discrete-Time Stochastic Neural Networks with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Wei Kang ◽  
Jun Cheng ◽  
Xiangyang Cheng
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequalities ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for discrete-time stochastic neural networks with time-varying delays is investigated in this paper. New delay-dependent passivity conditions are obtained in terms of linear matrix inequalities. Less conservative conditions are obtained by using integral inequalities to aid in the achievement of criteria ensuring the positiveness of the Lyapunov-Krasovskii functional. At last, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delays

2011 ◽  
Vol 21 (1) ◽  
pp. 127-135 ◽  
Author(s):  
Ramachandran Raja ◽  
Rathinasamy Sakthivel ◽  
Selvaraj Anthoni ◽  
Hyunsoo Kim
Keyword(s):  
Neural Networks ◽  
Hopfield Neural Networks ◽  
Markovian Switching ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stability Criteria ◽  
Markovian Jumping ◽  
Discrete State ◽  
Delay Dependent

Stability of impulsive Hopfield neural networks with Markovian switching and time-varying delaysThe paper is concerned with stability analysis for a class of impulsive Hopfield neural networks with Markovian jumping parameters and time-varying delays. The jumping parameters considered here are generated from a continuous-time discrete-state homogenous Markov process. By employing a Lyapunov functional approach, new delay-dependent stochastic stability criteria are obtained in terms of linear matrix inequalities (LMIs). The proposed criteria can be easily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A numerical example is provided to show that the proposed results significantly improve the allowable upper bounds of delays over some results existing in the literature.

scholarly journals New Results on Passivity Analysis of Delayed Discrete-Time Stochastic Neural Networks

2009 ◽  
Vol 2009 ◽  
pp. 1-17
Author(s):  
Jianjiang Yu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Passivity Analysis ◽  
Delay Dependent

The problem of passivity analysis for a class of discrete-time stochastic neural networks (DSNNs) with time-varying interval delay is investigated. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities (LMIs). The results are shown to be generalization of some previous results and are less conservative than the existing works. Meanwhile, the computational complexity of the obtained stability conditions is reduced because less variables are involved. Two numerical examples are given to show the effectiveness and the benefits of the proposed method.

Synchronization of Uncertain Neural Networks with performance and Mixed Time-Delays

2011 ◽  
pp. 261-288
Author(s):  
Hamid Reza Karimi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Mixed Time Delays ◽  
Initial States ◽  
Delayed State Feedback ◽  
Delay Dependent

An exponential H8 synchronization method is addressed for a class of uncertain master and slave neural networks with mixed time-delays, where the mixed delays comprise different neutral, discrete and distributed time-delays. An appropriate discretized Lyapunov-Krasovskii functional and some free weighting matrices are utilized to establish some delay-dependent sufficient conditions for designing a delayed state-feedback control as a synchronization law in terms of linear matrix inequalities under less restrictive conditions. The controller guarantees the exponential H8 synchronization of the two coupled master and slave neural networks regardless of their initial states. Numerical simulations are provided to demonstrate the effectiveness of the established synchronization laws.

scholarly journals State Estimation for Neural Networks with Leakage Delay and Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jing Liang ◽  
Zengshun Chen ◽  
Qiankun Song
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Time Varying Delay ◽  
General Activation ◽  
Delay Dependent ◽  
Error State

The state estimation problem is investigated for neural networks with leakage delay and time-varying delay as well as for general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing matrix inequality techniques, a delay-dependent linear matrix inequalities (LMIs) condition is developed to estimate the neuron state with some observed output measurements such that the error-state system is globally asymptotically stable. An example is given to show the effectiveness of the proposed criterion.

A DELAY-DEPENDENT APPROACH TO ROBUST PASSIVITY ANALYSIS FOR TAKAGI-SUGENO FUZZY UNCERTAIN RECURRENT NEURAL NETWORKS WITH MIXED INTERVAL TIME-VARYING DELAYS

2013 ◽  
Vol 21 (03) ◽  
pp. 415-433 ◽  
Author(s):  
K. H. TSENG ◽  
J. S. H. TSAI ◽  
C. Y. LU
Keyword(s):  
Neural Networks ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Interval Time ◽  
Passivity Analysis ◽  
Fuzzy Neural ◽  
Delay Dependent

This paper deals with the passivity analysis problem for Takagu-Sugeno (T-S) fuzzy neural networks with mixed interval time-varying delays and uncertain parameters. The time delays comprise discrete and distributed interval time-varying delays and the uncertain parameters are norm-bounded. Delay-dependent sufficient conditions for the passivity problem are obtained by using Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique. The important feature of the results lies in that it does not make use of upper bounds to introduce some degree of conservativeness. Two illustrative examples are exploited in order to illustrate the effectiveness of the proposed design procedures.

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