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 Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Differential System ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Impulsive Effects ◽  
Stability Criteria ◽  
Mixed Time Delays ◽  
The Stability ◽  
Stochastic Reaction

This paper is concerned with the stability of impulsive stochastic reaction-diffusion differential systems with mixed time delays. First, an equivalent relation between the solution of a stochastic reaction-diffusion differential system with time delays and impulsive effects and that of corresponding system without impulses is established. Then, some stability criteria for the stochastic reaction-diffusion differential system with time delays and impulsive effects are derived. Finally, the stability criteria are applied to impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed time delays, and sufficient conditions are obtained for the exponentialp-stability of the zero solution to the neural networks. An example is given to illustrate the effectiveness of our theoretical results. The systems we studied in this paper are more general, and some existing results are improved and extended.

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.

Stability Analysis for Discrete-Time Stochastic Neural Networks with Mixed Time Delays via Delay-Paritioning

2011 ◽  
Vol 228-229 ◽  
pp. 464-470
Author(s):  
Xia Zhou ◽  
Shou Ming Zhong
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Discrete Time ◽  
Time Delays ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Mixed Time Delays

This paper revisits the problem of stability analysis for discrete-time stochastic neural networks (DSNNs) with mixed time-varying delays in the state. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. A new delay-dependent stability criterion is presented by constructing a novel Lyapunov-Krasovskii functional and utilizing the delay partitioning idea and free-weighting matrix approach, Which is less conservative than the existing ones. This criterion can be developed in the frame of convex optimization problems and then solved via standard numerical software. These conditions are formulated in the forms of linear matrix inequalities, which feasibility can be easily checked by using Matlab LMI Toolbox.

scholarly journals Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
YaJun Li ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
The Novel ◽  
Free Weight ◽  
Fuzzy Neural ◽  
The Stability

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

scholarly journals Exponential Synchronization for Stochastic Neural Networks with Mixed Time Delays and Markovian Jump Parameters via Sampled Data

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yingwei Li ◽  
Xueqing Guo
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Stochastic Neural Networks ◽  
Sampled Data ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays ◽  
Data Controller

The exponential synchronization issue for stochastic neural networks (SNNs) with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI) approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

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.

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