scholarly journals Mean Square Stability of Impulsive Stochastic Differential Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shujie Yang ◽  
Bao Shi ◽  
Mo Li
Keyword(s):  
Stochastic Analysis ◽  
Functional Method ◽  
Stochastic Equations ◽  
Mean Square ◽  
Differential Systems ◽  
Numerical Examples ◽  
Mean Square Stability ◽  
Analysis Theory ◽  
Delay Dependent ◽  
Theoretical Results

Based on Lyapunov-Krasovskii functional method and stochastic analysis theory, we obtain some new delay-dependent criteria ensuring mean square stability of a class of impulsive stochastic equations. Numerical examples are given to illustrate the effectiveness of the theoretical results.

scholarly journals Analysis of Exponential Stability for Neutral Stochastic Cohen-Grossberg Neural Networks with Mixed Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Tianqing Yang ◽  
Zuoliang Xiong ◽  
Cuiping Yang
Keyword(s):  
Neural Networks ◽  
Stochastic Analysis ◽  
Stability Problem ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Mixed Delays ◽  
Mean Square ◽  
Analysis Theory ◽  
The Mean ◽  
Theoretical Results

This paper is concerned with the mean-square exponential input-to-state stability problem for a class of stochastic Cohen-Grossberg neural networks. Different from prior works, neutral terms and mixed delays are discussed in our system. By employing the Lyapunov-Krasovskii functional method, Itô formula, Dynkin formula, and stochastic analysis theory, we obtain some novel sufficient conditions to ensure that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are given to illustrate the correctness of the theoretical results.

scholarly journals Mean-Square Exponential Input-to-State Stability of Stochastic Fuzzy Recurrent Neural Networks with Multiproportional Delays and Distributed Delays

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Tianyu Wang ◽  
Quanxin Zhu ◽  
Jingwei Cai
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Stochastic Analysis ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Mean Square ◽  
Analysis Theory ◽  
Dynkin’S Formula ◽  
Theoretical Results

We are interested in a class of stochastic fuzzy recurrent neural networks with multiproportional delays and distributed delays. By constructing suitable Lyapunov-Krasovskii functionals and applying stochastic analysis theory, Ito^’s formula and Dynkin’s formula, we derive novel sufficient conditions for mean-square exponential input-to-state stability of the suggested system. Some remarks and discussions are given to show that our results extend and improve some previous results in the literature. Finally, two examples and their simulations are provided to illustrate the effectiveness of the theoretical results.

scholarly journals Mean-Square Stability of Milstein Methods for Stochastic Pantograph Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Feiyan Xiao ◽  
Tingting Qin ◽  
Chengjian Zhang
Keyword(s):  
Stability Criterion ◽  
Mean Square ◽  
Numerical Examples ◽  
Mean Square Stability ◽  
The Mean ◽  
Theoretical Results

This paper deals with nonlinear stochastic pantograph equations. For solving the equations, a class of extended Milstein methods are suggested. A mean-square stability criterion for this type of equations is presented. It is proved that under the suitable conditions the Milstein methods preserve the mean-square stability. Numerical examples further illustrate the obtained theoretical results.

scholarly journals Mean Square Consensus for Uncertain Multiagent Systems with Noises and Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yuangong Sun
Keyword(s):  
Multiagent Systems ◽  
Stochastic Analysis ◽  
Matrix Theory ◽  
Time Varying ◽  
Mean Square ◽  
Numerical Examples ◽  
Measurement Noises ◽  
Approximation Type ◽  
Theoretical Results ◽  
Mean Square Consensus

This paper investigates the consensus problem in mean square for uncertain multiagent systems with stochastic measurement noises and symmetric or asymmetric time-varying delays. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the convergence of a class of distributed stochastic approximation type protocols with time-varying consensus gains. Numerical examples are also given to illustrate the theoretical results.

A New Controller of Stochastic Delay Systems

2011 ◽  
Vol 63-64 ◽  
pp. 974-977
Author(s):  
Yun Chen ◽  
Qing Qing Li
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Mean Square ◽  
Closed Loop System ◽  
Stochastic Delay ◽  
Numerical Example ◽  
Mean Square Stability ◽  
Delay Dependent

By introducing an additional vector, a new delay-dependent controller is designed for stochastic systems with time delay in this paper. The presented controller is formulated by means of LMI, and it guarantees robust asymptotical mean-square stability of the resulting closed-loop system. Our result shows advantage over some existing ones, which is demonstrated by a numerical example.

scholarly journals Existence of Center for Planar Differential Systems with Impulsive Perturbations

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Dengguo Xu
Keyword(s):  
Computing Methods ◽  
Impulsive Systems ◽  
Differential Systems ◽  
Numerical Examples ◽  
State Dependent ◽  
Planar Systems ◽  
Linear And Nonlinear ◽  
Impulsive Perturbations ◽  
The Stability ◽  
Theoretical Results

We present a method that uses successor functions in ordinary differential systems to address the “center-focus” problem of a class of planar systems that have an impulsive perturbation. By deriving solution formulae for impulsive systems, several interesting criteria for distinguishing between the center and the focus of linear and nonlinear planar systems with state-dependent impulsions are established. The conditions describing the stability of the focus of the considered models are also given. The computing methods presented here are more convenient for determining the center of impulsive systems than those in the literature. Numerical examples are given to show the effectiveness of the theoretical results.

scholarly journals Finite-Time Passivity and Passification Design for Markovian Jumping Systems with Mode-Dependent Time-Varying Delays

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Ma
Keyword(s):  
Finite Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Varying ◽  
Markovian Jumping ◽  
Markovian Jumping Systems ◽  
The Mean ◽  
Delay Dependent ◽  
Passivity And Passification ◽  
Theoretical Results

This paper investigates the finite-time passivity and passification design problem for a class of Markovian jumping systems with mode-dependent time-varying delays. By employing the Lyapunov-Krasovskii functional method, delay-dependent sufficient criteria are derived to ensure the mean-square stochastically finite-time passivity. Based on the established results, mode-dependent passification controller is further designed in terms of linear matrix inequalities, such that the prescribed passive performance index of the resulting closed-loop system can be satisfied. Finally, two illustrative examples are given to show the effectiveness of the obtained theoretical results.

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