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.

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 Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Qiang Xi ◽  
Jianguo Si
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Sufficient Condition ◽  
Time Varying ◽  
Activation Functions ◽  
Mixed Time Delays

We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Robust Stabilization andH∞Control for Uncertain Neural Networks with Mixed Time Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Bin Wen ◽  
Hui Li ◽  
Li Liang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Time Delays ◽  
Convex Combination ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Uncertain Neural Networks

This paper is concerned with the problem of robust stabilization andH∞control for a class of uncertain neural networks. For the robust stabilization problem, sufficient conditions are derived based on the quadratic convex combination property together with Lyapunov stability theory. The feedback controller we design ensures the robust stability of uncertain neural networks with mixed time delays. We further design a robustH∞controller which guarantees the robust stability of the uncertain neural networks with a givenH∞performance level. The delay-dependent criteria are derived in terms of LMI (linear matrix inequality). Finally, numerical examples are provided to show the effectiveness of the obtained results.

scholarly journals Design of exponential state estimators for neutral-type neural networks with mixed time delays

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3435-3449
Author(s):  
Bo Du
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Estimation Error ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
The State ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
State Estimators ◽  
Exponentially Stable

In this paper, the state estimation problem is dealt with for a class of neutral-type neural networks with mixed time delays. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Lyapunov-Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.

scholarly journals Finite-Time Nonfragile Dissipative Control for Discrete-Time Neural Networks with Markovian Jumps and Mixed Time-Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Ling Hou ◽  
Dongyan Chen ◽  
Chan He
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Existence Condition ◽  
Mode Switching ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Time Varying Delay ◽  
Mixed Time Delays

This paper considers the stochastic finite-time dissipative (SFTD) control problem based on nonfragile controller for discrete-time neural networks (NNS) with Markovian jumps and mixed delays, in which the mode switching phenomenon, is described as Markov chain, and the mixed delays are composed of discrete time-varying delay and distributed delays. First, by selecting an appropriate Lyapunov-Krasovskii functional and applying stochastic analysis methods, some parameters-dependent sufficient conditions for solvability of stochastic finite-time boundedness are derived. Then, the main results are extended to SFTD control. Furthermore, existence condition of nonfragile controller is derived based on solution of linear matrix inequalities (LMIs). Finally, two numerical examples are employed to show the effectiveness of the obtained methods.

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 Stability in Switched Cohen-Grossberg Neural Networks with Mixed Time Delays and Non-Lipschitz Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Huaiqin Wu ◽  
Guohua Xu ◽  
Chongyang Wu ◽  
Ning Li ◽  
Kewang Wang ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Activation Functions ◽  
Mixed Time Delays ◽  
Switched Neural Networks ◽  
Exponentially Stable ◽  
The Stability ◽  
Delay Dependent

The stability for the switched Cohen-Grossberg neural networks with mixed time delays andα-inverse Hölder activation functions is investigated under the switching rule with the average dwell time property. By applying multiple Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) technique, a delay-dependent sufficient criterion is achieved to ensure such switched neural networks to be globally exponentially stable in terms of LMIs, and the exponential decay estimation is explicitly developed for the states too. Two illustrative examples are given to demonstrate the validity of the theoretical results.

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.

scholarly journals State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Lijie Geng ◽  
Haiying Li ◽  
Bingchen Zhao ◽  
Guang Su
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Discrete Time ◽  
Time Delays ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Fuzzy Cellular Neural Networks ◽  
Mixed Time Delays

This paper is concerned with the exponential state estimation problem for a class of discrete-time fuzzy cellular neural networks with mixed time delays. The main purpose is to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. By constructing a novel Lyapunov-Krasovskii functional which contains a triple summation term, some sufficient conditions are derived to guarantee the existence of the state estimator. The linear matrix inequality approach is employed for the first time to deal with the fuzzy cellular neural networks in the discrete-time case. Compared with the present conditions in the form ofM-matrix, the results obtained in this paper are less conservative and can be checked readily by the MATLAB toolbox. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed results.

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