scholarly journals Dynamics of Uncertain Discrete-Time Neural Network with Delay and Impulses

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xuehui Mei ◽  
Liwei Zhang ◽  
Haijun Jiang ◽  
Zhiyong Yu
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Discrete Time ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Conservative Condition ◽  
Impulsive Delay ◽  
The Stability

The stability of discrete-time impulsive delay neural networks with and without uncertainty is investigated. First, by using Razumikhin-type theorem, a new less conservative condition for the exponential stability of discrete-time neural network with delay and impulse is proposed. Moreover, some new sufficient conditions are derived to guarantee the stability of uncertain discrete-time neural network with delay and impulse by using Lyapunov function and linear matrix inequality (LMI). Finally, several examples with numerical simulation are presented to demonstrate the effectiveness of the obtained results.

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.

scholarly journals Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Wen-Jer Chang ◽  
Bo-Jyun Huang ◽  
Po-Hsun Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Control Technique ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Ship Steering

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

scholarly journals Stability Analysis for Discrete-Time Stochastic Fuzzy Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
YaJun Li ◽  
Quanxin Zhu
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Neural Networks ◽  
Linear Matrix ◽  
Mixed Delays ◽  
The Novel ◽  
Free Weight ◽  
Fuzzy Neural ◽  
The Stability

This paper is concerned with the stability problem of a class of discrete-time stochastic fuzzy neural networks with mixed delays. New Lyapunov-Krasovskii functions are proposed and free weight matrices are introduced. The novel sufficient conditions for the stability of discrete-time stochastic fuzzy neural networks with mixed delays are established in terms of linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate the effectiveness and benefits of the proposed method.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

Switching Control for a Class of Discrete-Time Switched Fuzzy Systems Based on LMI

2014 ◽  
Vol 945-949 ◽  
pp. 2543-2546
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Discrete Time ◽  
Fuzzy Systems ◽  
Sufficient Conditions ◽  
Switching Control ◽  
Linear Matrix ◽  
Common Lyapunov Function ◽  
Lyapunov Function Method ◽  
The Common ◽  
The Stability ◽  
Stability Issues

Switching control and stability issues for discrete-time switched systems whose subsystems are all discrete-time fuzzy systems are studied and new results derived. Innovated representation models for switched fuzzy systems are proposed. The common Lyapunov function method has been adopted to study the stability of this class of switched fuzzy systems. Sufficient conditions for asymptotic stability are presented. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

STABILITY ANALYSIS FOR DELAYED CELLULAR NEURAL NETWORKS BASED ON LINEAR MATRIX INEQUALITY APPROACH

2004 ◽  
Vol 14 (09) ◽  
pp. 3377-3384 ◽  
Author(s):  
XIAOFENG LIAO ◽  
KWOK-WO WONG ◽  
SHIZHONG YANG
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Functional Differential ◽  
The Stability

Some sufficient conditions for the asymptotic stability of cellular neural networks with time delay are derived using the Lyapunov–Krasovskii stability theory for functional differential equations as well as the linear matrix inequality (LMI) approach. The analysis shows how some well-known results can be refined and generalized in a straightforward manner. Moreover, the stability criteria obtained are delay-independent. They are less conservative and restrictive than those reported so far in the literature, and provide a more general set of criteria for determining the stability of delayed cellular neural networks.

scholarly journals Robust Linear Neural Network for Constrained Quadratic Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Zixin Liu ◽  
Yuanan Liu ◽  
Lianglin Xiong
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Perturbation Theory ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Analysis Method ◽  
Linear Neural Network ◽  
Constrained Quadratic Optimization

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper.

scholarly journals RobustH∞Control for Discrete-Time Stochastic Interval System with Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shengchun Yu ◽  
Guici Chen ◽  
Yi Shen
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Delay System ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Time Delay System ◽  
Interval System ◽  
Uncertain Time ◽  
System With Time Delay

The robustH∞control problem for discrete-time stochastic interval system (DTSIS) with time delay is investigated in this paper. The stochastic interval system is equivalently transformed into a kind of stochastic uncertain time-delay system firstly. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the robustH∞controller for DTSIS are obtained in terms of linear matrix inequality (LMI) form, and the robustH∞controller is designed. Finally, a numerical example with simulation is given to show the effectiveness and correctness of the designed robustH∞controller.

Fuzzy Control of a Class of Discrete-Time Fuzzy Bilinear Systems with Time-Delay

2012 ◽  
Vol 482-484 ◽  
pp. 1881-1885
Author(s):  
Jian Hu Jiang ◽  
Chao Wu ◽  
Yun Wang Ge ◽  
Li Jun Song
Keyword(s):  
Discrete Time ◽  
Sufficient Conditions ◽  
Bilinear System ◽  
Stability Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay

The stability control problem is considered for a class of discrete-time T-S fuzzy bilinear system with time-varying delay in both state and input. Based on the parallel distribute compensation (PDC) scheme, some sufficient conditions are derived to guarantee the global asymptotically stability of the overall fuzzy system, which are represented in terms of matrix inequality. The corresponding controller can be obtained by solving a set of linear matrix inequalities. Finally, a simulation example shows that the approach is effective.

Fuzzy-Model-Based Adaptive Control for a Kind of Discrete-Time Systems with Time-Delay and Disturbances

2014 ◽  
Vol 22 (03) ◽  
pp. 453-468
Author(s):  
Yi-Min Li ◽  
Yuan-Yuan Li
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Model Based ◽  
The Stability

This paper presents the stability analysis of discrete-time fuzzy-model-based adaptive control systems with time-delay, parameter uncertainties and external disturbance. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discretetime nonlinear system. A fuzzy observer is used to estimate the state of the fuzzy system, by using the estimations of states and nonlinear functions, and sufficient conditions for designing observer-based fuzzy controllers are proposed. The control and observer matrices involved can be determined by solving a set of linear matrix inequality (LMI). Finally, the numerical example carried out also demonstrate the feasibility of the design method.

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