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.

scholarly journals State Estimation for Discrete-Time Takagi-Sugeno Fuzzy Systems with Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ting Lei ◽  
Qiankun Song ◽  
Yurong Liu
Keyword(s):  
State Estimation ◽  
Discrete Time ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Inequality Technique ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Error State

The state estimation problem is investigated for discrete-time Takagi-Sugeno fuzzy systems with time-varying delays. By constructing appropriate Lyapunov-Krasovskii functionals and employing matrix inequality technique, a delay-dependent linear matrix inequalities (LMIs) criterion is developed to estimate the systems state with some observed output measurements such that the error-state system is globally asymptotically stable. An example with simulations is given to show the effectiveness of the proposed criterion.

scholarly journals Improved Stability Criteria of Static Recurrent Neural Networks with a Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Lei Ding ◽  
Hong-Bing Zeng ◽  
Wei Wang ◽  
Fei Yu
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Improved Stability ◽  
The Stability ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
Varying Delay

This paper investigates the stability of static recurrent neural networks (SRNNs) with a time-varying delay. Based on the complete delay-decomposing approach and quadratic separation framework, a novel Lyapunov-Krasovskii functional is constructed. By employing a reciprocally convex technique to consider the relationship between the time-varying delay and its varying interval, some improved delay-dependent stability conditions are presented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the merits and the effectiveness of the proposed methods.

scholarly journals Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Qiankun Song ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Computationally Efficient ◽  
Inequality Technique ◽  
General Activation ◽  
Delay Dependent

The problems on global dissipativity and global exponential dissipativity are investigated for uncertain discrete-time neural networks with time-varying delays and general activation functions. By constructing appropriate Lyapunov-Krasovskii functionals and employing linear matrix inequality technique, several new delay-dependent criteria for checking the global dissipativity and global exponential dissipativity of the addressed neural networks are established in linear matrix inequality (LMI), which can be checked numerically using the effective LMI toolbox in MATLAB. Illustrated examples are given to show the effectiveness of the proposed criteria. It is noteworthy that because neither model transformation nor free-weighting matrices are employed to deal with cross terms in the derivation of the dissipativity criteria, the obtained results are less conservative and more computationally efficient.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Improved Delay-Dependent Stability Analysis for Neural Networks with Interval Time-Varying Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Upper And Lower Bounds ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Time Varying Delay ◽  
Improved Stability ◽  
Delay Dependent ◽  
Delay Partitioning

The problem of delay-dependent asymptotic stability analysis for neural networks with interval time-varying delays is considered based on the delay-partitioning method. Some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs) by constructing a new Lyapunov-Krasovskii functional (LKF) in each subinterval and combining with reciprocally convex approach. Moreover, our criteria depend on both the upper and lower bounds on time-varying delay and its derivative, which is different from some existing ones. Finally, a numerical example is given to show the improved stability region of the proposed results.

scholarly journals Stochastic Passivity of Uncertain Neural Networks with Time-Varying Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Jianting Zhou ◽  
Qiankun Song ◽  
Jianxi Yang
Keyword(s):  
Neural Networks ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Analysis Technique ◽  
Uncertain Neural Networks ◽  
Delay Dependent ◽  
Varying Delay

The passivity problem is investigated for a class of stochastic uncertain neural networks with time-varying delay as well as generalized activation functions. By constructing appropriate Lyapunov-Krasovskii functionals, and employing Newton-Leibniz formulation, the free-weighting matrix method, and stochastic analysis technique, a delay-dependent criterion for checking the passivity of the addressed neural networks is established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. An example with simulation is given to show the effectiveness and less conservatism of the proposed criterion. It is noteworthy that the traditional assumptions on the differentiability of the time-varying delays and the boundedness of its derivative are removed.

scholarly journals Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sreten Stojanovic ◽  
Milan Stojanovic ◽  
Milos Stevanovic
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Varying ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Reciprocally Convex Combination ◽  
Delay Dependent ◽  
Delay Dependent Stability

The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

scholarly journals New Results on Passivity Analysis of Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-18
Author(s):  
YaJun Li ◽  
Zhaowen Huang
Keyword(s):  
Neural Networks ◽  
Leakage Delay ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Analysis Theory ◽  
Delay Dependent ◽  
The Impact ◽  
Varying Delay

The passivity problem for a class of stochastic neural networks systems (SNNs) with varying delay and leakage delay has been further studied in this paper. By constructing a more effective Lyapunov functional, employing the free-weighting matrix approach, and combining with integral inequality technic and stochastic analysis theory, the delay-dependent conditions have been proposed such that SNNs are asymptotically stable with guaranteed performance. The time-varying delay is divided into several subintervals and two adjustable parameters are introduced; more information about time delay is utilised and less conservative results have been obtained. Examples are provided to illustrate the less conservatism of the proposed method and simulations are given to show the impact of leakage delay on stability of SNNs.

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