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.

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 RobustH∞Filtering for Uncertain Neutral Stochastic Systems with Markovian Jumping Parameters and Time Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Yajun Li ◽  
Zhaowen Huang
Keyword(s):  
Time Delay ◽  
Stochastic Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Stochastically Stable ◽  
Neutral Stochastic Systems ◽  
Error System ◽  
Delay Dependent

This paper deals with the robustH∞filter design problem for a class of uncertain neutral stochastic systems with Markovian jumping parameters and time delay. Based on the Lyapunov-Krasovskii theory and generalized Finsler Lemma, a delay-dependent stability condition is proposed to ensure not only that the filter error system is robustly stochastically stable but also that a prescribedH∞performance level is satisfied for all admissible uncertainties. All obtained results are expressed in terms of linear matrix inequalities which can be easily solved by MATLAB LMI toolbox. Numerical examples are given to show that the results obtained are both less conservative and less complicated in computation.

scholarly journals RobustH∞Control of Uncertain T-S Fuzzy Time-Delay System: A Delay Decomposition Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Cheng Gong ◽  
Chunsong Han
Keyword(s):  
Time Delay ◽  
Delay System ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Decomposition Approach ◽  
System A ◽  
Delay Decomposition Approach ◽  
Uncertain Time ◽  
Delay Dependent ◽  
Delay Decomposition

This paper is concerned with the problem of robustH∞control for a class of uncertain time-delay fuzzy systems with norm-bounded parameter uncertainties. By utilizing the instrumental idea of delay decomposition, the decomposed Lyapunov-Krasovskii functional is introduced to uncertain T-S fuzzy system, and some delay-dependent conditions for the existence of robust controller are formulated in the form of linear matrix inequalities (LMIs). When these LMIs are feasible, a controller is presented. A numerical example is given to demonstrate the effectiveness of the proposed method.

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.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals H∞Filtering for Discrete Markov Jump Singular Systems with Mode-Dependent Time Delay Based on T-S Fuzzy Model

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Cheng Gong ◽  
Yi Zeng
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Singular Systems ◽  
Fuzzy Model ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Markov Jump ◽  
Markov Jump Systems ◽  
Delay Dependent ◽  
Jump Systems

This paper investigates theH∞filtering problem of discrete singular Markov jump systems (SMJSs) with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition onH∞-disturbance attenuation is presented, in which both stability and prescribedH∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependentH∞filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

Delay-Dependent L1 Filtering for LPV Systems With Parameter-Varying Delays

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Yanhui Li ◽  
Yan Liang ◽  
Xionglin Luo
Keyword(s):  
Filter Design ◽  
Peak Performance ◽  
Linear Matrix ◽  
Compact Set ◽  
Worst Case ◽  
Lpv Systems ◽  
Error System ◽  
Parameter Varying ◽  
Space Data ◽  
Delay Dependent

The paper investigates the problems of delay-dependent L1 filtering for linear parameter-varying (LPV) systems with parameter-varying delays, in which the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rate. The attention is focused on the design of L1 filter that guarantees the filtering error system to be asymptotically stable and satisfies the worst-case peak-to-peak gain of the filtering error system. In particular, we concentrate on the delay-dependent case, using parameter-dependent Lyapunov function, the decoupled peak-to-peak performance criterion is first established for a class of LPV systems. Under this condition, the admissible filter can be found in terms of linear matrix inequality (LMI) technology. According to approximate basis function and the gridding technique, the filter design problem is transformed into feasible solution problem of the finite parameter LMIs. Finally, a numerical example is provided to illustrate the feasibility of the developed approach.

scholarly journals T-S Fuzzy Model-Based Approximation and Filter Design for Stochastic Time-Delay Systems with Hankel Norm Criterion

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yanhui Li ◽  
Xiujie Zhou
Keyword(s):  
Time Delay ◽  
Filter Design ◽  
Fuzzy Model ◽  
Lyapunov Stability Theory ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Hankel Norm ◽  
Error System ◽  
Stochastic Time

This paper investigates the Hankel norm filter design problem for stochastic time-delay systems, which are represented by Takagi-Sugeno (T-S) fuzzy model. Motivated by the parallel distributed compensation (PDC) technique, a novel filtering error system is established. The objective is to design a suitable filter that guarantees the corresponding filtering error system to be mean-square asymptotically stable and to have a specified Hankel norm performance levelγ. Based on the Lyapunov stability theory and the Itô differential rule, the Hankel norm criterion is first established by adopting the integral inequality method, which can make some useful efforts in reducing conservativeness. The Hankel norm filtering problem is casted into a convex optimization problem with a convex linearization approach, which expresses all the conditions for the existence of admissible Hankel norm filter as standard linear matrix inequalities (LMIs). The effectiveness of the proposed method is demonstrated via a numerical example.

scholarly journals Quantized passive filtering for switched delayed neural networks

2021 ◽  
Vol 26 (1) ◽  
pp. 93-112
Author(s):  
Youmei Zhou ◽  
Yajuan Liu ◽  
Jianping Zhou ◽  
Zhen Wang
Keyword(s):  
Neural Networks ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Passive Filter ◽  
Delayed Neural Networks ◽  
Noise Interference ◽  
Exponentially Stable ◽  
Error System ◽  
Inequality Techniques

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods.

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