scholarly journals Exponential Stability Analysis and Application of Parameters Switched Neural Networks Via Intermittent Observation and Feedback Control

2021 ◽  
Author(s):  
Xianghui Zhou ◽  
Zizong Yan ◽  
Fanchao Kong ◽  
Wuneng Zhou
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Stability Control ◽  
Matched Pair ◽  
Analysis Method ◽  
Switched Neural Networks ◽  
Main System ◽  
Contraction Map ◽  
Uniqueness Of The Solution ◽  
The Stability

Abstract This paper deals with a type of the exponential stability problem for the switched neural networks with timevarying delays driven by Brownian noise. As a prerequisite to main theorem, the existence and uniqueness of the solution to the main system are proved via contraction map theory. Based on intermittent observation control, the stability trajectory of the switched neural networks with time-varying delays is obtained. Employing stochastic analysis method, the exponential stability conditions are established via applying It^o formula and the matched pair technique. A numerical example for the main system with respect to intermittent observation control is provided to illustrate the effectiveness of results and potential of the proposed techniques. Meanwhile, the feasibility of stability control in multiagents system is verified by the method obtained.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

scholarly journals LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Ruofeng Rao ◽  
Xiongrui Wang ◽  
Shouming Zhong ◽  
Zhilin Pu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Schur Complement ◽  
Great Difficulty ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Almost Sure Exponential Stability ◽  
The Stability ◽  
Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

String Exponential Stability With Mode Constraint of Stochastic Vehicle Following Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Lan Tang
Keyword(s):  
Exponential Stability ◽  
Sufficient Conditions ◽  
Original System ◽  
Analysis Method ◽  
Geometrical Analysis ◽  
Stochastic Disturbance ◽  
Infinite Dimensional ◽  
Vector Lyapunov Function ◽  
Lyapunov Function Method ◽  
The Stability

Associated with automatic vehicle following system is the problem of the stability of a platoon of vehicles. The stability with mode constraint is the property of damping disturbances as they travel away from the source in the system. In this paper, a class of infinite-dimensional vehicle longitudinal following system with stochastic disturbance is analyzed. By applying geometrical analysis method, a lemma for analyzing the stability of generalized vector comparison inequalities with respect to the original systems is established. With the help of the lemma, some sufficient conditions for assuring the string exponential stability with mode constraint of the original system are obtained by applying vector Lyapunov function method. The obtained conditions are less conservative than the existing ones. A numerical example is given to show the effectiveness of the established conditions.

scholarly journals Robust Exponential Stability Analysis of Switched Neural Networks with Interval Parameter Uncertainties and Time Delays

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Xiaohui Xu ◽  
Huanbin Xue ◽  
Yiqiang Peng ◽  
Jiye Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Delays ◽  
Average Dwell Time ◽  
Interval Parameter ◽  
Parameter Uncertainties ◽  
Robust Exponential Stability ◽  
Switched Neural Networks ◽  
Globally Exponential Stability ◽  
Arbitrary Switching

In this paper, the stability of switched neural networks (SNNs) with interval parameter uncertainties and time delays is investigated. First, the conditions for the existence and uniqueness of the equilibrium point of the system are discussed. Second, the average dwell time approach and M-matrix property are employed to obtain conditions to ensure the globally exponential stability of the delayed SNNs under constrained switching. Third, by resorting to inequality technique and the idea of vector Lyapunov function, sufficient condition to ensure the robust exponential stability of the delayed SNNs under arbitrary switching is derived. The form of the constructed Lyapunov functions is simple, which has certain commonality in studying delayed SNNs, and the proposed results not only are explicit but also reveal the relationship between the constrained switching and the arbitrary switching of the SNNs. Finally, two numerical examples are presented to illustrate the effectiveness and less conservativeness of the main results compared with the existing literature.

scholarly journals Globally Exponential Stability of Impulsive Neural Networks with Given Convergence Rate

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chengyan Liu ◽  
Xiaodi Li ◽  
Xilin Fu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Convergence Rate ◽  
Exponential Stability ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
Analysis Techniques ◽  
Globally Exponential Stability ◽  
The Stability

This paper deals with the stability problem for a class of impulsive neural networks. Some sufficient conditions which can guarantee the globally exponential stability of the addressed models with given convergence rate are derived by using Lyapunov function and impulsive analysis techniques. Finally, an example is given to show the effectiveness of the obtained results.

scholarly journals Fixed Points and Exponential Stability for Impulsive Time-Delays BAM Neural Networks via LMI Approach and Contraction Mapping Principle

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Ruofeng Rao ◽  
Zhilin Pu ◽  
Shouming Zhong ◽  
Xinggui Li
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Exponential Stability ◽  
Time Delays ◽  
Large Scale ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Bam Neural Networks ◽  
Lmi Approach ◽  
The Stability

The fixed point technique has been employed in the stability analysis of time-delays bidirectional associative memory (BAM) neural networks with impulse. By formulating a contraction mapping in a product space, a new LMI-based exponential stability criterion was derived. Lately, fixed point methods have educed various good results inspiring this work, but those criteria cannot be programmed by a computer. In this paper, LMI conditions of the obtained result can be applicable to computer Matlab LMI toolbox which meets the need of the large-scale calculation in real engineering. Moreover, a numerical example and a comparable table are presented to illustrate the effectiveness of the proposed methods.

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