Design of exponential state estimators for neutral-type neural networks with 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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Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

Canadian Journal of Physics ◽

10.1139/p10-086 ◽

2010 ◽

Vol 88 (12) ◽

pp. 885-898 ◽

Cited By ~ 20

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.

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

Mathematical Problems in Engineering ◽

10.1155/2015/690578 ◽

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.

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

Gaming and Simulations ◽

10.4018/978-1-60960-195-9.ch420 ◽

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.

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

Discrete Dynamics in Nature and Society ◽

10.1155/2012/435402 ◽

2012 ◽

Vol 2012 ◽

pp. 1-21 ◽

Cited By ~ 3

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.

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

Chaos Synchronization and Cryptography for Secure Communications - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-61520-737-4.ch012 ◽

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.

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Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays

Abstract and Applied Analysis ◽

10.1155/2012/236562 ◽

2012 ◽

Vol 2012 ◽

pp. 1-21 ◽

Cited By ~ 2

Author(s):

Weiyuan Zhang ◽

Junmin Li ◽

Minglai Chen

Keyword(s):

Neural Networks ◽

Time Delays ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Linear Matrix ◽

Mixed Time Delays ◽

Dynamical Behaviors ◽

Proposed Model ◽

The Mean ◽

Stochastic Reaction

We discuss the dynamical behaviors of impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with mixed time delays. By using a well-knownL-operator differential inequality with mixed time delays and combining with the Lyapunov-Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction-diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.

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On Complex Artificial Higher Order Neural Networks

Artificial Higher Order Neural Networks for Economics and Business ◽

10.4018/978-1-59904-897-0.ch021 ◽

2009 ◽

pp. 466-843 ◽

Cited By ~ 3

Author(s):

Zidong Wang ◽

Yurong Liu ◽

Xiaohui Liu

Keyword(s):

Neural Networks ◽

Time Delay ◽

Exponential Stability ◽

Discrete Time ◽

Time Delays ◽

Higher Order ◽

Linear Matrix ◽

Mixed Time Delays ◽

Exponentially Stable ◽

Higher Order Neural Networks

This chapter deals with the analysis problem of the global exponential stability for a general class of stochastic artificial higher order neural networks with multiple mixed time delays and Markovian jumping parameters. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. The main purpose of this chapter is to establish easily verifiable conditions under which the delayed high-order stochastic jumping neural network is exponentially stable in the mean square in the presence of both the mixed time delays and Markovian switching. By employing a new Lyapunov-Krasovskii functional and conducting stochastic analysis, a linear matrix inequality (LMI) approach is developed to derive the criteria ensuring the exponential stability. Furthermore, the criteria are dependent on both the discrete time-delay and distributed time-delay, hence less conservative. The proposed criteria can be readily checked by using some standard numerical packages such as the Matlab LMI Toolbox. A simple example is provided to demonstrate the effectiveness and applicability of the proposed testing criteria.

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

Abstract and Applied Analysis ◽

10.1155/2014/327070 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 1

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.

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DELAY-DEPENDENT ROBUST EXPONENTIAL STABILITY FOR UNCERTAIN RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

International Journal of Neural Systems ◽

10.1142/s012906570700107x ◽

2007 ◽

Vol 17 (03) ◽

pp. 207-218 ◽

Cited By ~ 39

Author(s):

BAOYONG ZHANG ◽

SHENGYUAN XU ◽

YONGMIN LI

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Recurrent Neural Networks ◽

Sufficient Conditions ◽

Linear Matrix ◽

Time Varying ◽

Parameter Uncertainties ◽

Robust Exponential Stability ◽

Neuron Activation ◽

Exponentially Stable

This paper considers the problem of robust exponential stability for a class of recurrent neural networks with time-varying delays and parameter uncertainties. The time delays are not necessarily differentiable and the uncertainties are assumed to be time-varying but norm-bounded. Sufficient conditions, which guarantee that the concerned uncertain delayed neural network is robustly, globally, exponentially stable for all admissible parameter uncertainties, are obtained under a weak assumption on the neuron activation functions. These conditions are dependent on the size of the time delay and expressed in terms of linear matrix inequalities. Numerical examples are provided to demonstrate the effectiveness and less conservatism of the proposed stability results.

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