Exponential Stability of Markovian Jumping Memristor-Based Neural Networks via Event-Triggered Impulsive Control Scheme

The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

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Exponential Stability for Delayed Stochastic Bidirectional Associative Memory Neural Networks with Markovian Jumping and Impulses

Journal of Optimization Theory and Applications ◽

10.1007/s10957-011-9817-3 ◽

2011 ◽

Vol 158 (1) ◽

pp. 251-273 ◽

Cited By ~ 11

Author(s):

R. Sakthivel ◽

R. Raja ◽

S. M. Anthoni

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Associative Memory ◽

Bidirectional Associative Memory ◽

Markovian Jumping

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LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

Journal of Applied Mathematics ◽

10.1155/2013/396903 ◽

2013 ◽

Vol 2013 ◽

pp. 1-21 ◽

Cited By ~ 3

Author(s):

Ruofeng Rao ◽

Xiongrui Wang ◽

Shouming Zhong ◽

Zhilin Pu

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Functional Differential Equations ◽

Schur Complement ◽

Great Difficulty ◽

Markovian Jumping ◽

Robust Exponential Stability ◽

Almost Sure Exponential Stability ◽

The Stability ◽

Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

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Sliding Intermittent Control for BAM Neural Networks with Delays

Abstract and Applied Analysis ◽

10.1155/2013/615947 ◽

2013 ◽

Vol 2013 ◽

pp. 1-15 ◽

Cited By ~ 3

Author(s):

Jianqiang Hu ◽

Jinling Liang ◽

Hamid Reza Karimi ◽

Jinde Cao

Keyword(s):

Neural Networks ◽

Control Method ◽

Impulsive Control ◽

Intermittent Control ◽

Bam Neural Networks ◽

Periodically Intermittent Control ◽

Control Scheme ◽

Special Cases ◽

Exponentially Stable ◽

Continuous Feedback

This paper addresses the exponential stability problem for a class of delayed bidirectional associative memory (BAM) neural networks with delays. A sliding intermittent controller which takes the advantages of the periodically intermittent control idea and the impulsive control scheme is proposed and employed to the delayed BAM system. With the adjustable parameter taking different particular values, such a sliding intermittent control method can comprise several kinds of control schemes as special cases, such as the continuous feedback control, the impulsive control, the periodically intermittent control, and the semi-impulsive control. By using analysis techniques and the Lyapunov function methods, some sufficient criteria are derived for the closed-loop delayed BAM neural networks to be globally exponentially stable. Finally, two illustrative examples are given to show the effectiveness of the proposed control scheme and the obtained theoretical results.

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