随机脉冲控制下超混沌复Lü系统的渐近稳定性

基于脉冲微分方程的稳定性理论,研究了具有随机信号的脉冲作用下,超混沌复Lü系统的渐近稳定性.给出了确定性和随机脉冲作用下系统达到渐近稳定的判据.并且提出了在等距脉冲间隔下,系统达到稳定的区域估计值.通过数值算例,讨论了确定性脉冲和随机脉冲的异同点,并证实,此方法对于外界噪声是比较稳健的.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

噪声环境中时滞双向联想记忆神经网络指数稳定

任何系统实际上都是在噪声环境中进行工作的.对处在噪声强度已知的噪声环境下双向联想记忆(BAM)神经网络,其平衡点具有指数渐近稳定性是网络进行异联想记忆的基础.构造一个适当的Lyapunov函数,应用It^o公式、M矩阵等工具讨论了在噪声环境下具有时滞的BAM神经网络概率1指数渐近稳定,得到了指数稳定的代数判据和两个推论,此判据只需验证仅由网络参数构成的矩阵是M矩阵即可,给网络设计带来方便.本文所得结果包括相关文献中确定性结果作为特例.     

动态神经网络的输入2状态稳定性分析

针对非自治的动态神经网络系统，建立了动态神经网络的数学模型．并将其等效成一个非线性仿射控制系统．深入分析了该系统平衡点的存在性、唯一性和全局渐近稳定性，给出了系统输入-状态稳定的充分条件，构建了ISS-Lyapunov函数，并应用该函数确保了系统的全局渐近稳定性．     

一类多延时多变量网络控制系统的建模及稳定性

针对一类多延时多变量网络控制系统（NCS）,讨论其建模和稳定性问题．首先假设传感器采用时间驱动、控制器和执行器采用事件驱动,建立了系统在连续时域~MIMO数学模型;然后根据Lyapunov稳定性原理和Razumikhin定理,构造系统的Lyapunov函数,并分析系统的渐近稳定性,进而得到了系统稳定的时延参数和稳定性条件;最后通过仿真实例验证了该类网络控制系统的稳定判据．     

具有有色噪声的线性随机系统的矩稳定性

研究具有有色噪声的线性随机系统的矩稳定性,得到了无需计算矩阵方根的矩阵特征值代数判据,并用实例演示了文中的方法。     

参数摄动混杂离散系统的鲁棒稳定性

采用线性矩阵不等式(LMI)方法研究离散事件状态转移条件为状态依赖的参数摄动线性混杂离散系统的鲁棒稳定性问题, 提出此类系统全局鲁棒渐近稳定性判定定理, 基于分段Lyapunov函数给出了一般混杂离散系统在Lyapunov意义下局部稳定的判定定理, 该定理可将线性混杂离散系统的稳定性问题转化为LMI问题, 在此基础上提出了参数摄动线性混杂离散系统在Lyapunov意义下局部鲁棒稳定的充分条件.     

切换线性时滞系统的稳定性判据

考虑了一类切换线性时滞系统的稳定性问题.基于Lyapunov函数方法和矩阵测度的概念,分别给出了切换系统时滞独立以及时滞依赖的渐近稳定性和指数稳定性判据,设计了相应的镇定切换律.最后,通过数值算例验证了所提算法的正确有效性.     

测度型时变区间脉冲大系统的稳定性

本文首次提出并研究了测度型线性时变区间脉冲大系统的稳定性问题。利用比较原理等方法，借助于线性时变和线性定常无脉冲系统的稳定性，建立了相应的线性时变区间脉冲大系统的全局指数稳定性判据。     

具有可变时滞的中立型随机系统的渐近性质

本文研究了一类具有可变时滞的中立型随机系统解的渐近性质.利用Lyapunov函数It、^o公式和上鞅收敛定理,得到了该系统解的一些几乎必然渐近稳定性与p阶均值渐近稳定性、几乎必然多项式渐近稳定性与p阶均值多项式渐近稳定性及几乎必然指数稳定性与p阶均值指数稳定性的充分判据.与经典的随机稳定性结论相比,本文所建立的判据充分利用了随机扰动项的作用,无须LV(扩散算子)的负定.     

Stability analysis for a class of random nonlinear impulsive systems

In this paper, the problem of noise‐to‐state stability (NSS) and globally asymptotic stability (GAS) is investigated for a class of nonlinear systems with random disturbances and impulses, where the random noises have finite second‐order moments and the so‐called random impulses mean that impulse ranges are driven by a sequence of random variables. First, some general conditions are given to guarantee the existence and uniqueness of solutions to random nonlinear impulsive systems. Next, when the continuous dynamics are stable but the impulses are destabilizing, the NSS and GAS of random nonlinear impulsive systems are examined by the average impulsive interval approach. Then, when the continuous dynamics are unstable but the impulses are stabilizing, it is shown that the NSS and GAS can be retained by using the reverse average impulsive interval approach. Finally, the theoretical findings are substantiated with illustrative examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Moment exponential stability of stochastic nonlinear delay systems with impulse effects at random times

In this paper, we investigate the pth moment exponential stability for a class of impulsive stochastic functional differential equations with impulses at random times. The impulsive times considered in this paper are random times that are different from those investigated in the existing literature. By using the stochastic process theory, stochastic analysis theory, Razumikhin technique, and Lyapunov method, we obtain some new criteria of the pth moment exponential stability for the related system. Finally, some examples are provided to show the effectiveness of the theoretical results.     

Stability of Hybrid Impulsive and Switching Stochastic Systems with Time-delay

This paper investigates a model of hybrid impulsive and switching stochastic systems (HISSS) with time-delay. Several stability criteria, including the globally asymptotical and exponential stability criteria in the pth moment and mean square, are established by using Itô formula, a generalized switching Lyapunov functions and some relating techniques. Especially, a more general Lyapunov-Krasivskii functional is constructed, and it is observed that the mean square asymptotic and exponential stability conditions of HISSS are delay-dependent. A numerical example shows that the obtained stability results can reduce the conservativeness.     

关联噪声对线性系统信噪比的影响

研究了关联白噪声对具有偏置信号测制噪声的线性模型的信噪比的影响,通过计算噪声的指数形式的积分,推导出了一阶矩、相关函数和信噪比的精确解析表达式,并且发现加性噪声能够增强信噪比,而乘性噪声使信噪比减小,噪声之间的关联性能够使信噪比增大,增强输出的信号强度,该结果可应用于光通信系统,对改善输出信号的质量有应用价值。     

Asymptotic stability of impulsive high-order Hopfield type neural networks

In this paper, we discuss impulsive high-order Hopfield type neural networks. Investigating their global asymptotic stability, by using Lyapunov function method, sufficient conditions that guarantee global asymptotic stability of networks are given. These criteria can be used to analyse the dynamics of biological neural systems or to design globally stable artificial neural networks. Two numerical examples are given to illustrate the effectiveness of the proposed method.     

Variational Bayesian inference based robust multiple measurement sparse signal recovery

This work concentrates on not only probing into a novel Bayesian probabilistic model to formulate a general type of robust multiple measurement vectors sparse signal recovery problem with impulsive noise, but also developing an improved variational Bayesian method to recover the original joint row sparse signals. In the design of the model, two three-level hierarchical Bayesian estimation procedures are designed to characterize impulsive noise and joint row sparse source signals by means of Gaussian scale mixtures and multivariate generalized t distribution. Those hidden variables, included in signal and measurement models are estimated based on a variational Bayesian framework, in which multiple kinds of probability distributions are adopted to express their features. In the design of the algorithm, the proposed algorithm is a full Bayesian inference approach related to variational Bayesian estimation. It is robust to impulsive noise, since the posterior distribution estimation can be effectively approached through estimating unknown parameters. Extensive simulation results show that the proposed algorithm significantly outperforms the compared robust sparse signal recovery approaches under different kinds of impulsive noises.     

Delay-dependent stability analysis for impulsive neural networks with time varying delays

In this paper, the global exponential stability and global asymptotic stability of the neural networks with impulsive effect and time varying delays is investigated. By using Lyapunov–Krasovskii-type functional, the quality of negative definite matrix and Cauchy criterion, we obtain the sufficient conditions for global exponential stability and global asymptotic stability of such model, in terms of linear matrix inequality (LMI), which depend on the delays. Two examples are given to illustrate the effectiveness of our theoretical results.     

带相关噪声、随机观测滞后和丢失的随机不确定系统的最优线性估值器

对带有限步相关噪声、乘性噪声、多步随机观测滞后和丢失的复杂网络化控制系统,根据相关噪声的步数,分析了噪声和状态、噪声和观测、噪声和新息、观测和新息、状态和新息之间的相关性,给出了相关阵的递推计算公式.利用射影理论,提出了线性最小方差最优线性估值器,包括滤波器、预报器和平滑器.一个网络监测环境下的三容器水箱系统的实例仿真,验证了算法的有效性.     

On the stability of uncertain systems with multiple time-varyingdelays

In this paper, criteria for the global asymptotic stability of a class of uncertain systems with multiple time-varying delays are proposed. Based on the improved Razumikhin-type theorem, delay-dependent and delay-independent criteria are provided to guarantee the global asymptotic stability of such systems. Our main results are generalizations of some recent results reported in the literature in the case with multiple time-varying delays. A numerical example Is also given to illustrate our results     

On hybrid impulsive and switching systems and application to nonlinear control

In this note, a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated. Using switched Lyapunov functions, some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established. In addition, a new hybrid impulsive and switching control strategy for nonlinear systems is developed. A typical example, the unified chaotic system, is given to illustrate the theoretical results.