Stabilization of stochastic delayed neural networks with Markovian switching

In this paper, the mean square exponential stabilization problem is investigated for a class of stochastic delayed neural networks with Markovian switching. After proposing an exponential stability condition, our attention is focused on the design of a state feedback controller such that the stochastic delayed neural networks with Markovian switching is exponentially stable in mean square. Several stabilization criteria, delay‐independent and delay‐dependent ones, which are expressed in terms of a set of linear matrix inequalities (LMIs), are proposed to stabilize the stochastic delayed neural networks with Markovian switching exponentially. The usefulness and applicability of the developed results are illustrated by means of two numerical examples. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Attractor and Stochastic Boundedness for Stochastic Infinite Delay Neural Networks with Markovian Switching

First, we establish the stochastic LaSalle theorem for stochastic infinite delay differential equations with Markovian switching, from which some criterias on attraction are obtained. Then, by employing Lyapunov method and LaSalle-type theorem established above, we obtain some sufficient conditions ensuring the attractor and stochastic boundedness for stochastic infinite delay neural networks with Markovian switching. Finally, an example is also discussed to illustrate the efficiency of the obtained results.     

具有时滞的脉冲随机神经网络的有限时间稳定性

本文研究具有时滞的脉冲随机神经网络的有限时间稳定性问题.利用Lyapunov泛函技术,线性矩阵不等式(LMIs)工具和平均脉冲区间条件,对反镇定型、中立型和镇定型3种类型的脉冲系统分别给出了基于矩阵不等式的有限时间均方稳定的充分条件,最后通过一个数值例子验证了理论结果的有效性.     

Global asymptotic stability of delay BAM neural networks with impulses via nonsmooth analysis

In this paper, we study global asymptotic stability of delay bi-directional associative memory (BAM) neural networks with impulses. We obtain a sufficient condition of ensuring existence and uniqueness of equilibrium point for delay BAM neural networks with impulses basing on nonsmooth analysis. And we give a criteria of global asymptotic stability of the unique equilibrium point for delay BAM neural networks with impulses using Lyapunov method. At last, we present examples to illustrate that our results are feasible.     

Exponential ultimate boundedness of impulsive stochastic delay difference systems

This paper is concerned with the exponential ultimate boundedness problems for the impulsive stochastic delay difference systems. Several sufficient conditions on the global pth moment exponential ultimate boundedness are presented by using the Lyapunov methods and the algebraic inequality techniques, and the estimated exponential convergence rate and the ultimate bound are provided as well. As an application, the boundedness criteria are applied to a class of discrete impulsive stochastic neural networks with delays. The obtained results show that the impulses not only can stabilize an unstable stochastic difference delay system but also can make an unbounded stochastic difference delay system into a bounded system. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.     

Finite-time annular domain stability of Itô stochastic impulsive systems with markovian jumping under asynchronous switching

ABSTRACT

This study examines the finite time annular domain stability (FTADS) and stabilisation of a class of Itô stochastic impulsive systems with asynchronous switching controller. The asynchronous switching means that the controller switching does not accurately coincide with system switching in delayed time interval. The design of the controller depends on the observed jumping parameters, which cannot be precisely measured in real-time because of switching delay. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. When the subsystem is stable in the synchronous switching interval and unstable in the asynchronous case, a compromise among the average impulsive interval, the upper bound of delay, and the decay/increasing rate of Lyapunov function in the synchronous/asynchronous switching interval respectively is given. By the mode-dependent parameter approach (MDPA) and allowing the increase of the impulses on all the switching times, the extended FTADS criteria for Itô stochastic impulsive systems in generally nonlinear setting are derived first. Then, we focus on the case when the system in both synchronous and asynchronous switching intervals are unstable. By reaching a tradeoff among average impulsive interval, the upper bound of delay, the magnitude of impulses and the difference between the increasing rate of Lyapunov function in the synchronous and asynchronous switching interval, new sufficient conditions for existence of the state feedback controller are also developed by MDPA. In addition, we consider the effect of different impulsive strengths (harmful and beneficial impulses) and obtained less conservative results because the Lyapunov function may be non-decreasing during switching interval. Moreover, we extend the conclusion from nonlinear stochastic impulsive switching systems to linear case. Finally, we present two examples to illustrate the effectiveness of the results obtained in this study.     

Impulsive Control for a Class of Cellular Neural Networks with Proportional Delay

This paper is concerned with a class of cellular neural networks with proportional delay and impulses. First, by employing the improved Razumikhin technique and Lyapunov functions, some delay-dependent criteria are established to guarantee asymptotic stability and global stability of a class of general impulsive differential equations with proportional delay. Second, applying the obtained criteria, we get some delay-dependent sufficient conditions ensuring the existence, uniqueness and globally asymptotic stability of the equilibrium point of the cellular neural networks with proportional delay and impulses presented in this paper. Finally, three examples are presented to illustrate the effectiveness and advantages of the results obtained.     

On the exponential synchronization of stochastic impulsive chaotic delayed neural networks

In this paper, the exponential synchronization of stochastic impulsive chaotic delayed neural networks is investigated. Based on the Lyapunov function method, time-varying delay feedback control technique and the efficient modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical chaotic delayed neural networks with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Comparing with the existing works that consider single perturbation (stochastic or impulsive one), the proposed method can provide a more general framework for the synchronization of multi-perturbation chaotic systems, which is favorable for practical application in secure communication. Finally, numerical simulations verify the effectiveness of the proposed method.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Exponential Synchronization of Stochastic Fuzzy Cellular Neural Networks with Reaction-Diffusion Terms via Periodically Intermittent Control

This paper considers the exponential synchronization of stochastic fuzzy cellular neural networks with time-varying delays and reaction-diffusion terms based on p-norm. Motivated by the achievements from both the stability of fuzzy cellular neural networks with stochastic perturbation and reaction-diffusion effects and the synchronization issue of coupled chaotic delayed neural networks by using periodically intermittent control approach, a periodically intermittent controller is proposed to guarantee the exponential synchronization of the coupled chaotic neural networks by using Lyapunov stability theory and stochastic analysis approaches. The synchronization results presented in this paper generalize and improve many known results. This paper also presents an illustrative example and uses simulated results of this example to show the feasibility and effectiveness of the proposed scheme.     

Almost Sure Exponential Stability of Recurrent Neural Networks With Markovian Switching

This paper presents new stability results for recurrent neural networks with Markovian switching. First, algebraic criteria for the almost sure exponential stability of recurrent neural networks with Markovian switching and without time delays are derived. The results show that the almost sure exponential stability of such a neural network does not require the stability of the neural network at every individual parametric configuration. Next, both delay-dependent and delay-independent criteria for the almost sure exponential stability of recurrent neural networks with time-varying delays and Markovian-switching parameters are derived by means of a generalized stochastic Halanay inequality. The results herein include existing ones for recurrent neural networks without Markovian switching as special cases. Finally, simulation results in three numerical examples are discussed to illustrate the theoretical results.     

Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control

This paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results.     

Synchronization in Quaternion-Valued Neural Networks with Delay and Stochastic Impulses

Neural Processing Letters - A class of global exponential synchronization problem for delayed quaternion-valued neural networks with stochastic impulses has been investigated in this paper, where...     

Robust H∞ performance for discrete time T-S fuzzy switched memristive stochasticneural networks with mixed time-varying delays

ABSTRACT

In this paper, we study the robust H _∞ performance for discrete-time T-S fuzzy switched memristive stochastic neural networks with mixed time-varying delays and switching signal design. The neural network under consideration is subject to time-varying and norm bounded parameter uncertainties. Decomposing of the delay interval approach is employed in both the discrete delays and distributed delays. By constructing a proper Lyapunov-Krasovskii functional (LKF) with triple summation terms and using an improved summation inequality techniques. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to guarantee the considered discrete-time neural networks to be exponentially stable. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the developed theoretical results.     

Passivity analysis of stochastic delayed neural networks with Markovian switching

In this paper, the problem of passivity analysis is investigated for a class of stochastic delayed neural networks with Markovian switching. By applying Lyapunov functional and free-weighting matrix, delay-dependent/independent passivity criteria are presented in terms of linear matrix inequalities. The results herein include existing ones for neural networks without Markovian switching as special cases. An example is given to demonstrate the effectiveness of the proposed criteria.     

Stabilization of stochastic Markovian switching systems on networks with multilinks based on aperiodically intermittent control: A new differential inequality technique

In this paper, the stabilization problem of stochastic Markovian switching systems on networks with multilinks and time‐varying delays (SMNMT) is investigated via aperiodically intermittent control. At first, a new differential inequality is established for SMNMT, which relaxes the conditions of time‐varying delays compared with existing literature. Different from previous approaches of studying multilinks systems, new differential inequality technique combined with graph theory and Lyapunov method is adopted, based on which two types of sufficient conditions are derived to ensure the stability of SMNMT. The topological structure of multilinks systems on networks, stochastic perturbation, the transition rate of Markov chain, and intermittent control has a great impact on these developed conditions. The theoretical results are applied to stochastic Markovian switching oscillators networks with multilinks (SMONM), and a stabilization criterion of SMONM is derived as well. Finally, a numerical example is shown to illustrate the feasibility of our theoretical results.     

随机时滞神经网络的全局指数稳定性

首先对一般随机系统的渐近特性进行了讨论.然后结合神经网络的特点,应用李雅普诺夫第二方法对一类随机时滞神经网络系统的全局指数稳定性进行了分析,给出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,并给出实例进行仿真实验.     

Synchronization of unknown chaotic neural networks with stochastic perturbation and time delay in the leakage term based on adaptive control and parameter identification

In this paper, we investigate the synchronization problem of chaotic neural networks with unknown parameters, stochastic perturbation and time delay in the leakage term. A simple and robust adaptive controller is designed such that the response system can be synchronized with a drive system with unknown parameters by utilizing Lyapunov stability theory and parameter identification. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. This research also demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks

This paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete-time neural networks with time-varying delay. The individual neural network is subject to parameter uncertainty, stochastic disturbance, and time-varying delay, where the norm-bounded parameter uncertainties exist in both the state and weight matrices, the stochastic disturbance is in the form of a scalar Wiener process, and the time delay enters into the activation function. For the array of coupled neural networks, the constant coupling and delayed coupling are simultaneously considered. We aim to establish easy-to-verify conditions under which the addressed neural networks are synchronized. By using the Kronecker product as an effective tool, a linear matrix inequality (LMI) approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally, robustly, exponentially synchronized in the mean square. The LMI-based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time-varying delay, and can be solved efficiently via the Matlab LMI Toolbox. Two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme.      

具有时滞脉冲的线性随机时滞系统的均方指数稳定

本文研究了具有时滞脉冲的线性随机时滞系统的稳定性问题,基于Lyapunov函数和Razumikhin技巧,针对具有镇定型脉冲和反镇定型脉冲的线性随机时滞系统分别建立了系统均方指数稳定的充分条件,最后给出两个数值例子论证结果的有效性.