scholarly journals Delay-Dependent Exponential Stability for Uncertain Neutral Stochastic Systems with Mixed Delays and Markovian Jumping Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Huabin Chen
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Mixed Delays ◽  
Time Varying ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Globally Exponential Stability ◽  
Neutral Stochastic Systems ◽  
Delay Dependent ◽  
Stability In Mean Square

This paper is mainly concerned with the globally exponential stability in mean square of uncertain neutral stochastic systems with mixed delays and Markovian jumping parameters. The mixed delays are comprised of the discrete interval time-varying delays and the distributed time delays. Taking the stochastic perturbation and Markovian jumping parameters into account, some delay-dependent sufficient conditions for the globally exponential stability in mean square of such systems can be obtained by constructing an appropriate Lyapunov-Krasovskii functional, which are given in the form of linear matrix inequalities (LMIs). The derived criteria are dependent on the upper bound and the lower bound of the time-varying delay and the distributed delay and are therefore less conservative. Two numerical examples are given to illustrate the effectiveness and applicability of our obtained results.

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.

Robust Exponential Stability of Stochastic Discrete-Time BAM Neural Networks with Markovian Jumping Parameters and Delays

2014 ◽  
Vol 989-994 ◽  
pp. 1877-1882 ◽  
Author(s):  
Liang Dong Guo ◽  
Jin Nie ◽  
You Shan Zhang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Linear Matrix ◽  
Bam Neural Networks ◽  
Markovian Jumping Parameters ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Globally Exponential Stability ◽  
Delay Dependent

The problem of robustly globally exponential stability in the mean square is investigated for stochastic uncertain discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays and Markovian jumping parameters. The uncertainties are assumed to be the linear fractional form. By using Lyapunov-Krasovskii functional (LKF) method and some novel technique, a delay-dependent exponential stability criterion is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and the improvement of the proposed methods.

Exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay

2018 ◽  
Vol 41 (2) ◽  
pp. 350-365 ◽  
Author(s):  
Xin Zhang ◽  
Huashan Liu ◽  
Yiyuan Zheng ◽  
Yuqing Sun ◽  
Wuneng Zhou ◽  
...  
Keyword(s):  
Exponential Stability ◽  
Lyapunov Functions ◽  
Stochastic Systems ◽  
Transition Probabilities ◽  
Time Varying ◽  
Analysis Method ◽  
Multiple Lyapunov Functions ◽  
Time Varying Delay ◽  
Neutral Stochastic Systems ◽  
Varying Delay

This paper discusses the problem of exponential stability for Markovian neutral stochastic systems with general transition probabilities and time-varying delay. Based on non-convolution type multiple Lyapunov functions and stochastic analysis method, we obtain the conditions which are independent to any decay rate of the exponential stability for uncertain transition probabilities neutral stochastic systems with time-varying delay. Finally, two examples are presented to illustrate the effectiveness and potential of the proposed results.

scholarly journals Delay-Dependent Robust Exponential Stability for Uncertain Neutral Stochastic Systems with Interval Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Weihua Mao ◽  
Feiqi Deng ◽  
Anhua Wan
Keyword(s):  
Exponential Stability ◽  
Stochastic Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Mean Square ◽  
Robust Exponential Stability ◽  
Interval Time ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
Delay Dependent

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities (LMIs). By free-weight matrices method, the usual restriction that the stability conditions only bear slow-varying derivative of the delay is removed. Finally, numerical examples are provided to illustrate the effectiveness of the proposed method.

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