On Robust Stability for Stochastic Neural Networks of Neutral-Type with Uncertainties and Time-Varying Delays

2012 ◽  
Vol 457-458 ◽  
pp. 716-722
Author(s):  
Guo Quan Liu ◽  
Simon X. Yang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Stability Criteria ◽  
Analysis Problem ◽  
Analysis Technique ◽  
Robust Stability Analysis

This paper is concerned with the robust stability analysis problem for stochastic neural networks of neutral-type with uncertainties and time-varying delays. Novel stability criteria are proposed in terms of linear matrix inequality (LMI) by defining a Lyapunov-Krasovskii functional and using the stochastic analysis technique. Two examples are given to show the effectiveness of the obtained conditions.

Delay-Range-Dependent Robust Stability for Uncertain Stochastic Neural Networks with Time-Varying Delays

2012 ◽  
pp. 418-432
Author(s):  
Wei Feng ◽  
Haixia Wu
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Stochastic Analysis ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Stability Criteria ◽  
Robust Stability Analysis ◽  
Uncertain Stochastic Neural Networks

This paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. By utilizing a Lyapunov-Krasovskii functional and conducting stochastic analysis, the authors show that the addressed neural networks are globally, robustly, and asymptotically stable if a convex optimization problem is feasible. Some stability criteria are derived for all admissible uncertainties, and these stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be effectively solved by some standard numerical packages. Five numerical examples are given to demonstrate the usefulness of the proposed robust stability criteria.

Delay-Range-Dependent Robust Stability for Uncertain Stochastic Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2 (4) ◽  
pp. 45-59
Author(s):  
Wei Feng ◽  
Haixia Wu
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Optimization Problem ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Stability Criteria ◽  
Convex Optimization Problem ◽  
Robust Stability Analysis ◽  
Uncertain Stochastic Neural Networks

This paper is concerned with the robust stability analysis problem for uncertain stochastic neural networks with interval time-varying delays. By utilizing a Lyapunov-Krasovskii functional and conducting stochastic analysis, the authors show that the addressed neural networks are globally, robustly, and asymptotically stable if a convex optimization problem is feasible. Some stability criteria are derived for all admissible uncertainties, and these stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI), which can be effectively solved by some standard numerical packages. Five numerical examples are given to demonstrate the usefulness of the proposed robust stability criteria.

New results of robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters1The work of authors was supported by Department of Science and Technology, New Delhi, India, under the sanctioned No. SR/S4/MS:485/07.

2011 ◽  
Vol 89 (8) ◽  
pp. 827-840 ◽  
Author(s):  
S. Lakshmanan ◽  
P. Balasubramaniam
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Robust Stability ◽  
Neutral Type ◽  
Linear Matrix ◽  
New Delhi ◽  
Time Varying ◽  
Markovian Jumping ◽  
Decomposition Approach ◽  
Robust Stability Analysis

In this paper, robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters is conducted. By using the delay-decomposition approach, a new Lyapunov–Krasovskii functional is constructed. Based on this Lyapunov–Krasovskii functional and some stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the effectiveness and reduced conservatism of our theoretical results.

scholarly journals Improved Delay-Dependent Robust Stability Criteria for a Class of Uncertain Neutral Type Lur’e Systems with Discrete and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Kaibo Shi ◽  
Hong Zhu ◽  
Shouming Zhong ◽  
Yong Zeng ◽  
Yuping Zhang
Keyword(s):  
Robust Stability ◽  
Neutral Type ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Lur’E Systems ◽  
Robust Stability Analysis ◽  
Delay Dependent ◽  
Delay Dependent Stability

This paper is concerned with the problem of delay-dependent robust stability analysis for a class of uncertain neutral type Lur’e systems with mixed time-varying delays. The system has not only time-varying uncertainties and sector-bounded nonlinearity, but also discrete and distributed delays, which has never been discussed in the previous literature. Firstly, by employing one effective mathematical technique, some less conservative delay-dependent stability results are established without employing the bounding technique and the mode transformation approach. Secondly, by constructing an appropriate new type of Lyapunov-Krasovskii functional with triple terms, improved delay-dependent stability criteria in terms of linear matrix inequalities (LMIs) derived in this paper are much brief and valid. Furthermore, both nonlinearities located in finite sector and infinite one have been also fully taken into account. Finally, three numerical examples are presented to illustrate lesser conservatism and the advantage of the proposed main results.

Delay-dependent robust stability criteria for stochastic neural networks of neutral-type with interval time-varying delay and linear fractional uncertainties

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
GUOQUAN LIU ◽  
SIMON X. YANG ◽  
YI CHAI ◽  
WEI FU
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Neutral Type ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Stability Criteria ◽  
Interval Time ◽  
Time Varying Delay ◽  
Delay Dependent ◽  
Varying Delay

In this paper, we investigate the problem of robust stability for a class of delayed neural networks of neutral-type with linear fractional uncertainties. The activation functions are assumed to be unbounded, non-monotonic and non-differentiable, and the delay is assumed to be time-varying and belonging to a given interval, which means that the lower and upper bounds of the interval time-varying delay are available. By constructing a general form of the Lyapunov–Krasovskii functional, and using the linear matrix inequality (LMI) approach, we derive several delay-dependent stability criteria in terms of LMI. Finally, we give a number of examples to illustrate the effectiveness of the proposed method.

scholarly journals Robust Stability Analysis of Neutral-Type Hybrid Bidirectional Associative Memory Neural Networks with Time-Varying Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Wei Feng ◽  
Simon X. Yang ◽  
Haixia Wu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Associative Memory ◽  
Robust Stability ◽  
Neutral Type ◽  
Time Varying ◽  
Bidirectional Associative Memory ◽  
Numerical Examples ◽  
Network Parameters ◽  
Robust Stability Analysis

The global asymptotic robust stability of equilibrium is considered for neutral-type hybrid bidirectional associative memory neural networks with time-varying delays and parameters uncertainties. The results we obtained in this paper are delay-derivative-dependent and establish various relationships between the network parameters only. Therefore, the results of this paper are applicable to a larger class of neural networks and can be easily verified when compared with the previously reported literature results. Two numerical examples are illustrated to verify our results.

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