Exponential Stability in Mean Square of Singular Markovian Jump System with Saturating Actuators and Time-Varying Delay

This paper investigates exponential stability in mean square of singular Markovian jump systems with saturating actuators and time-varying delay. The statistical property of the Markov process is fully used to derive the differential of the function. By using a delay decomposition method, a mode-dependent Lyapunov-Krasovskii function is established. A sufficient condition is proposed for exponential stability in mean square of the system designing the memoryless state feedback. A numerical example shows that the approach proposed is effective.

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Exponential stability in mean-square of Markovian jump stochastic bilinear systems with saturating actuators and time-varying delay

2012 Third International Conference on Intelligent Control and Information Processing ◽

10.1109/icicip.2012.6391531 ◽

2012 ◽

Author(s):

Xianfa Jiao ◽

Zongrun Liu

Keyword(s):

Exponential Stability ◽

Bilinear Systems ◽

Time Varying ◽

Mean Square ◽

Markovian Jump ◽

Time Varying Delay ◽

Saturating Actuators ◽

Varying Delay ◽

Stability In Mean Square

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Mean-square exponential stability for a class of discrete-time nonlinear singular Markovian jump systems with time-varying delay

Journal of the Franklin Institute ◽

10.1016/j.jfranklin.2014.07.013 ◽

2014 ◽

Vol 351 (10) ◽

pp. 4688-4723 ◽

Cited By ~ 11

Author(s):

Shaohua Long ◽

Shouming Zhong

Keyword(s):

Exponential Stability ◽

Discrete Time ◽

Time Varying ◽

Mean Square ◽

Markovian Jump ◽

Time Varying Delay ◽

Singular Markovian Jump Systems ◽

Mean Square Exponential Stability ◽

Jump Systems ◽

Varying Delay

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Stability Analysis and RobustH∞Control of Switched Stochastic Systems with Time-Varying Delay

Journal of Applied Mathematics ◽

10.1155/2012/202916 ◽

2012 ◽

Vol 2012 ◽

pp. 1-17 ◽

Cited By ~ 1

Author(s):

Zhengrong Xiang ◽

Guoxin Chen

Keyword(s):

Exponential Stability ◽

Stochastic Systems ◽

Average Dwell Time ◽

Linear Matrix ◽

Time Varying ◽

Mean Square ◽

Time Varying Delay ◽

Switched Stochastic Systems ◽

Mean Square Exponential Stability ◽

Varying Delay

The problems of mean-square exponential stability and robustH∞control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities (LMIs). Then,H∞performance is studied and robustH∞controller is designed. Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.

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Mean-Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-Varying Delay

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.760-762.1742 ◽

2013 ◽

Vol 760-762 ◽

pp. 1742-1747

Author(s):

Jin Fang Han

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Cellular Neural Networks ◽

Time Varying ◽

Mean Square ◽

Razumikhin Theorem ◽

Time Varying Delay ◽

Mean Square Exponential Stability ◽

The Mean ◽

Varying Delay

This paper is concerned with the mean-square exponential stability analysis problem for a class of stochastic interval cellular neural networks with time-varying delay. By using the stochastic analysis approach, employing Lyapunov function and norm inequalities, several mean-square exponential stability criteria are established in terms of the formula and Razumikhin theorem to guarantee the stochastic interval delayed cellular neural networks to be mean-square exponential stable. Some recent results reported in the literatures are generalized. A kind of equivalent description for this stochastic interval cellular neural networks with time-varying delay is also given.

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