scholarly journals Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Manlika Rajchakit ◽  
Grienggrai Rajchakit
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Stochastic System ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Mean Square ◽  
Interval Time ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Delay Dependent

This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

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.

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

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.

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 Exponential Stability of Stochastic Systems with Delay and Poisson Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Wenli Zhu ◽  
Jiexiang Huang ◽  
Zhao Zhao
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Mean Square ◽  
Poisson Jumps ◽  
Stochastic Delay ◽  
Exponentially Stable ◽  
The Mean

This paper focuses on the model of a class of nonlinear stochastic delay systems with Poisson jumps based on Lyapunov stability theory, stochastic analysis, and inequality technique. The existence and uniqueness of the adapted solution to such systems are proved by applying the fixed point theorem. By constructing a Lyapunov function and using Doob’s martingale inequality and Borel-Cantelli lemma, sufficient conditions are given to establish the exponential stability in the mean square of such systems, and we prove that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. The obtained results show that if stochastic systems is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic delay systems with Poisson jumps will remain exponentially stable, and time delay upper limit is solved by using the obtained results when the system is exponentially stable, and they are more easily verified and applied in practice.

scholarly journals Stability Analysis of Cohen–Grossberg Neural Networks with Random Impulses

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 144 ◽  
Author(s):  
Ravi Agarwal ◽  
Snezhana Hristova ◽  
Donal O’Regan ◽  
Peter Kopanov
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Direct Lyapunov Method ◽  
Time Varying ◽  
External Bias ◽  
Random Impulses ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
The Stability

The Cohen and Grossberg neural networks model is studied in the case when the neurons are subject to a certain impulsive state displacement at random exponentially-distributed moments. These types of impulses significantly change the behavior of the solutions from a deterministic one to a stochastic process. We examine the stability of the equilibrium of the model. Some sufficient conditions for the mean-square exponential stability and mean exponential stability of the equilibrium of general neural networks are obtained in the case of the time-varying potential (or voltage) of the cells, with time-dependent amplification functions and behaved functions, as well as time-varying strengths of connectivity between cells and variable external bias or input from outside the network to the units. These sufficient conditions are explicitly expressed in terms of the parameters of the system, and hence, they are easily verifiable. The theory relies on a modification of the direct Lyapunov method. We illustrate our theory on a particular nonlinear neural network.

scholarly journals Exponential Stability and Robust H∞ Control for Discrete-Time Time-Delay Infinite Markov Jump Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Yueying Liu ◽  
Ting Hou
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Mean Square ◽  
Markov Jump ◽  
Multiplicative Noises ◽  
Exogenous Disturbance ◽  
Mean Square Exponential Stability

In this paper, exponential stability and robust H∞ control problem are investigated for a class of discrete-time time-delay stochastic systems with infinite Markov jump and multiplicative noises. The jumping parameters are modeled as an infinite-state Markov chain. By using a novel Lyapunov-Krasovskii functional, a new sufficient condition in terms of matrix inequalities is derived to guarantee the mean square exponential stability of the equilibrium point. Then some sufficient conditions for the existence of feedback controller are presented to guarantee that the resulting closed-loop system has mean square exponential stability for the zero exogenous disturbance and satisfies a prescribed H∞ performance level. Numerical simulations are exploited to validate the applicability of developed theoretical results.

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