scholarly journals Robust H-infinity State Estimation of Uncertain Neural Networks with Two Additive Time-Varying Delays

2020 ◽  
Author(s):  
Xiaoping Hu ◽  
Yajun Wang ◽  
Jiakai Ding ◽  
Dongming Xiao
Keyword(s):  
Numerical Simulation ◽  
Neural Networks ◽  
State Estimation ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
H Infinity ◽  
Uncertain Neural Networks ◽  
Error System

This study is mainly concerned with the problem of robust H∞ state estimation of uncertain neural networks with two additive time-varying delays. A novel linear matrix inequalities (LMIs) is constructed based on Lyapunov-Krasovskii functionals (LKFs) which contains two additive time-varying delays components. LMIs method are used to estimate the derivative of LKFs, it is calculated that the derivative of the LKFs is smaller than zero, which proved that uncertain neural networks with two additive time-varying delays is globally asymptotically stable. Meantime, a stability criterion of error system is presented such that the HâĹđ performance is guaranteed. Finally, two numerical simulation examples have been performed to demonstrate the effectiveness of developed approach.

Delay-Dependent H∞ Filtering for Neural Networks with Time Delay

2014 ◽  
Vol 511-512 ◽  
pp. 875-879 ◽  
Author(s):  
Ya Jun Li ◽  
Yan Nong Liang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Filter Design ◽  
Linear Matrix ◽  
Globally Asymptotically Stable ◽  
H Infinity ◽  
Decomposition Approach ◽  
Delay Decomposition Approach ◽  
Error System ◽  
Delay Dependent

The H{infinity} filter design problem of recurrent neural networks with time delay is considered. Based on delay decomposition approach, the delay-dependent condition is derived to ensure that the filtering error system is globally asymptotically stable with a guaranteed performance. And the design of such a filter can be solved by the linear matrix inequality. A numerical example is provided to demonstrate that the developed approach is efficient.

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 Delay-Dependent State Estimation of Static Neural Networks with Time-Varying and Distributed Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Lei Shao ◽  
He Huang ◽  
Heming Zhao ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Lyapunov Functional ◽  
Estimation Error ◽  
Time Derivative ◽  
Distributed Delays ◽  
Linear Matrix ◽  
Time Varying ◽  
Globally Asymptotically Stable ◽  
Static Neural Networks

This paper focuses on studying the state estimation problem of static neural networks with time-varying and distributed delays. By constructing a suitable Lyapunov functional and employing two integral inequalities, a sufficient condition is obtained under which the estimation error system is globally asymptotically stable. It can be seen that this condition is dependent on the two kinds of time delays. To reduce the conservatism of the derived result, Wirtinger inequality is employed to handle a cross term in the time-derivative of Lyapunov functional. It is further shown that the design of the gain matrix of state estimator is transformed to finding a feasible solution of a linear matrix inequality, which is efficiently facilitated by available algorithms. A numerical example is explored to demonstrate the effectiveness of the developed result.

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

2011 ◽  
Vol 20 (04) ◽  
pp. 657-666
Author(s):  
CHOON KI AHN
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Estimation Error ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
State Estimator ◽  
Error System ◽  
Delay Dependent ◽  
Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

scholarly journals Stability Analysis and Robust H∞ Filtering for Discrete-time Nonlinear Systems with Time-varying Delays

2021 ◽  
Vol 20 ◽  
pp. 281-288
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Asymptotically Stable ◽  
Matrix Inequalities ◽  
Error System ◽  
Error Dynamics

In this paper, we investigate the problem of robust H∞ filter design for a class of discrete-time nonlinear systems. The systems under consider involves time-varying delays and parameters uncertainties. The main objective is to design a linear full-order filter to ensure that the resulting filtering error system is asymptotically stable with a prescribed H∞ performance level. By constructing an appropriate Lyapunov-Krasovskii functional, some novel sufficient conditions are established to guarantee the filter error dynamics system is robust asymptotically stable with H∞ performance γ , and the H∞ filter is designed in term of linear matrix inequalities. Finally, a numerical example is provided to illustrate the efficiency of proposed method.

scholarly journals Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Hongwen Xu ◽  
Huaiqin Wu ◽  
Ning Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
State Estimation ◽  
Time Delays ◽  
Estimation Error ◽  
Linear Matrix ◽  
Robust Exponential Stability ◽  
Interval Neural Networks ◽  
Distributed Time Delays ◽  
Error System

The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed time delays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Extended dissipative-based state estimation for Markov jump coupled neural networks with reaction-diffusion terms

2021 ◽  
pp. 014233122110282
Author(s):  
Dongxiao Hu ◽  
Xiaona Song ◽  
Xingru Li
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Dynamic Error ◽  
Signal Transmission ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Markov Jump ◽  
Memory Controller ◽  
Coupled Neural Networks ◽  
Error System

This work mainly concentrates on the state estimation for Markov jump coupled neural networks (MJCNNs) with reaction-diffusion terms, in which the memory controller is employed. First, the considered MJCNNs model is introduced, and the dynamic error system can be obtained based on the proposed state estimator. Then, a memory controller that involves constant signal transmission delay is designed. Moreover, by Lyapunov functional method, inequality technique and Kronecker product law, a novel stable and extended dissipative analysis criteria can be established to ensure that the stability of the error system the error system. Meanwhile, the controller gains can be obtained by solving linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the developed method.

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.

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.

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