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 Stability of Infinite Dimensional Interconnected Systems with Impulsive and Stochastic Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Xiaohui Xu ◽  
Xiaofeng Yin ◽  
Jiye Zhang ◽  
Peng Wang
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Sufficient Conditions ◽  
Interconnected Systems ◽  
Stochastic Disturbances ◽  
Infinite Dimensional ◽  
Disturbance Propagation ◽  
Vector Lyapunov Function ◽  
Look Ahead ◽  
The Stability

Some research on the stability with mode constraint for a class of infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances is studied by using the vector Lyapunov function approach. Intuitively, the stability with mode constraint is the property of damping disturbance propagation. Firstly, we derive a set of sufficient conditions to assure the stability with mode constraint for a class of general infinite dimensional look-ahead interconnected systems with impulsive and stochastic disturbances. The obtained conditions are less conservative than the existing ones. Secondly, the controller for a class of look-ahead vehicle following systems with the above uncertainties is constructed by the sliding mode control method. Based on the obtained new stability conditions, the domain of the control parameters of the systems is proposed. Finally, a numerical example with simulations is given to show the effectiveness and correctness 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.

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.

Exponential Stability of Stochastic Age-Dependent Population with Diffusion

2011 ◽  
Vol 282-283 ◽  
pp. 231-235
Author(s):  
Hui Li Han ◽  
Qi Min Zhang
Keyword(s):  
Hilbert Space ◽  
Exponential Stability ◽  
Dynamic System ◽  
Population Dynamic ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Exponential Martingale ◽  
Age Dependent ◽  
The Stability

In this paper, a class of stochastic age-dependent population dynamic system with diffusion is introduced. Exponential stability of paths of a strong solution for stochastic age-dependent population dynamic system in Hilbert space is established. The analyses use exponential martingale formula, Lyapunov functional and some special inequalities for our stability purposes. Various sufficient conditions are obtained to ensure the stability of the strong solutions. In particular, by means of our results we loosen the condition of stability.

scholarly journals Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Xiaohui Xu ◽  
Jibin Yang ◽  
Yanhai Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Mean Square ◽  
Integral Theorem ◽  
Stochastic Disturbance ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Complex Valued

This paper investigates the mean square exponential stability problem of a class of complex-valued neural networks with stochastic disturbance and mixed delays including both time-varying delays and continuously distributed delays. Under different assumption conditions concerning stochastic disturbance term from the existing ones, some sufficient conditions are derived for assuring the mean square exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and Ito^ differential-integral theorem. The obtained results not only generalize the existing ones, but also reduce the conservatism of the previous stability results about complex-valued neural networks with stochastic disturbances. Two numerical examples with simulation results are given to verify the feasibility of the proposed results.

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.

STABILITY ANALYSIS OF IMPULSIVE COHEN-GROSSBERG NEURAL NETWORK WITH UNBOUNDED DISCRETE TIME-VARYING DELAYS

2007 ◽  
Vol 17 (05) ◽  
pp. 407-417 ◽  
Author(s):  
QIANKUN SONG ◽  
JINDE CAO
Keyword(s):  
Neural Network ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Analysis Method ◽  
Inequality Technique ◽  
Stability Results

In this paper, the impulsive Cohen-Grossberg neural network with unbounded discrete time-varying delays is considered. By using the analysis method and inequality technique, several sufficient conditions are obtained to ensure the global exponential stability of the addressed neural network. These results generalize the existing relevant stability results. Two examples with simulations are given to show the effectiveness of the obtained results.

Global Exponential Stability of Cohen-Grossberg Neural Networks with Piecewise Constant Argument of Generalized Type and Impulses

2016 ◽  
Vol 28 (1) ◽  
pp. 229-255 ◽  
Author(s):  
Qiang Xi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Lyapunov Function Method ◽  
Generalized Type ◽  
Constant Argument

In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results.

scholarly journals Permanence and Periodic Solutions for a Two-Patch Impulsive Migration PeriodicN-Species Lotka-Volterra Competitive System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Analysis Method ◽  
Competitive System ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Globally Stable

We study a two-patch impulsive migration periodicN-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.

scholarly journals Exponential stability for delayed complex-valued neural networks with reaction-diffusion terms

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xiaohui Xu ◽  
Jibin Yang ◽  
Quan Xu ◽  
Yanhai Xu ◽  
Shulei Sun
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Reaction Diffusion ◽  
Mixed Delays ◽  
Lyapunov Function Method ◽  
Matrix Properties ◽  
The Stability ◽  
Homeomorphism Mapping ◽  
Complex Valued ◽  
Positive Effect

AbstractIn this study, we investigate reaction-diffusion complex-valued neural networks with mixed delays. The mixed delays include both time-varying and infinite distributed delays. Criteria are derived to ensure the existence, uniqueness, and exponential stability of the equilibrium state of the addressed system on the basis of the M-matrix properties and homeomorphism mapping theories as well as the vector Lyapunov function method. The results demonstrate the positive effect of reaction-diffusion on the stability, which further improves the existing conditions. Finally, the analysis of several examples is compared to the present results to verify the correctness and reduced conservatism of the primary results.

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