A novel approach on stabilization for linear systems with time-varying input delay

This paper presents new results on delay-dependent stability and stabilization for linear systems with interval time-varying delays. Some less conservative delay-dependent criteria for determining the stability of the time-delay systems are obtained in this paper. Based on the stability conditions, we propose a new state transformation technology to facilitate controller designing efficiently and computationally. The method is also applicable to the existing stability conditions reported by now, while the existing technologies may fail to derive computational control procedures from the stability conditions. Finally, some numerical examples well illustrate the effectiveness of the proposed method.     

常微分方程数值方的法稳定性(英)

本文针对常微分方程数值方法稳定性问题，证明了一般方法的绝对稳定性定理，同时也指出了绝对稳定性条件的局限性．为了克服这种局限性，本文绘出了Jordan稳定性的概念，并建立了一个相应的判别定理．     

Stability of Equilibria of Discrete-Time Systems and Localization of Invariant Compact Sets

The stability (or asymptotic stability) of equilibria of an time-invariant discrete-time system can be verified with the use of stability and asymptotic stability criteria stated in terms of invariant sets. An earlier proposed method reduces the verification of these criteria to some set operations. However, the method is analytical and hard to implement. We propose another approach to the verification of these criteria based on the functional method for localizing invariant compact sets.     

随机微分方程分步单支theta方法的稳定性(英文)

本文研究随机微分方程单支theta方法的均方稳定性.首先,对线性检验方程,当0≤θ<1时,分步单支theta方法在一定的步长限制下能保持原系统的均方稳定性,当θ=1时,方法按任意步长都能保持原系统的稳定性.其次,对满足单边Lipschitz条件的非线性随机微分方程,当1/2<θ0<θ<1时,方法能保持原系统的均方指数稳定性,但对步长有限制,如果θ=1,对步长限制消失.     

滞后型分段连续随机微分方程的稳定性

本文研究了滞后型分段连续随机微分方程的解析稳定性和数值稳定性问题.首先,利用伊藤公式等方法获得了解析解均方稳定的条件,其次,对于包括均方稳定和T-稳定在内的Euler-Maruyama方法的数值稳定性问题,运用不等式技术和随机分析方法获得了一些新的结果,证明了在一定条件下,Euler-Maruyama方法既是均方稳定又是T-稳定的,推广了随机延迟微分方程的数值稳定性结论.     

基于投影寻踪-随机森林的制造企业供应链稳定性评价

基于扎根理论提取制造企业供应链稳定性影响因素,鉴于因素的随机性和模糊性特征,引入云模型,将定性概念转化为定量数据,从众多影响因素中筛选出重要因素,构建制造企业供应链稳定性评价指标体系。采用加速遗传算法对建立的投影寻踪模型进行求解,确定指标权重与稳定性评价值。利用随机森林方法根据评价值划分供应链稳定性类型,检验评价方法科学性,并确定当前制造企业供应链稳定性的整体状态,据此提出优化制造企业供应链稳定性建议。     

同心圆管间无粘可压缩旋转流动的稳定性研究

本文主要研究了两个同心圆管之间无粘可压缩旋转流动的稳定性问题.首先推导出了关于径向扰动速度分量的可压缩线化微分方程.利用类似于Ludwieg的分析方法,推导了可压缩旋转流的两个稳定性准则.然后用有限差分方法数值求解了本征值问题,给出了时间增长率,并验证了稳定性准则的正确性.最后讨论了压缩性对稳定性的影响.     

Stability of implicit-explicit linear multistep methods for ordinary and delay differential equations

Stability properties of implicit-explicit (IMEX) linear multistep methods for ordinary and delay differential equations are analyzed on the basis of stability regions defined by using scalar test equations. The analysis is closely related to the stability analysis of the standard linear multistep methods for delay differential equations. A new second-order IMEX method which has approximately the same stability region as that of the IMEX Euler method, the simplest IMEX method of order 1, is proposed. Some numerical results are also presented which show superiority of the new method.      

Analytical and numerical methods for the stability analysis of linear fractional delay differential equations

In this paper, several analytical and numerical approaches are presented for the stability analysis of linear fractional-order delay differential equations. The main focus of interest is asymptotic stability, but bounded-input bounded-output (BIBO) stability is also discussed. The applicability of the Laplace transform method for stability analysis is first investigated, jointly with the corresponding characteristic equation, which is broadly used in BIBO stability analysis. Moreover, it is shown that a different characteristic equation, involving the one-parameter Mittag-Leffler function, may be obtained using the well-known method of steps, which provides a necessary condition for asymptotic stability. Stability criteria based on the Argument Principle are also obtained. The stability regions obtained using the two methods are evaluated numerically and comparison results are presented. Several key problems are highlighted.     

瞬态问题稳定性及弥散分析的无网格RKPM配点法研究

介绍了基于强形式的RKPM配点法求解瞬态动力问题的算法,并提出了采用RKPM配点法,配合时间域中心差分求解二阶波动方程的稳定性评价方法,并通过数值算例验证了此方法的正确性．此评价方法可以方便有效地评估出实际计算时的临界时间步长．通过数值算例比较可知,实际算例的计算临界时间步长与本评价方法,所预测的临界时间步长结果非常接近．给出了如何合理地选择RKPM形函数支撑域的建议．最后与径向基函数配点法进行了对比研究．     

Unique Continuation on Quadratic Curves for Harmonic Functions*

The unique continuation on quadratic curves for harmonic functions is discussed in this paper. By using complex extension method, the conditional stability of unique continuation along quadratic curves for harmonic functions is illustrated. The numerical algorithm is provided based on collocation method and Tikhonov regularization.The stability estimates on parabolic and hyperbolic curves for harmonic functions are demonstrated by numerical examples respectively.     

The stability problem for the torque-free gyrostat investigated by using algebraic methods

We apply an algebraic method for studying stability with respect to a set of conserved quantities for the problem of the torque-free gyrostat. If the conditions of this algebraic method are not fulfilled then the Lyapunov stability cannot be decided on using the specified set of conserved quantities.     

Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations

We consider the mean-square stability of the so-called improved split-step theta method for stochastic differential equations. First, we study the mean-square stability of the method for linear test equations with real parameters. When θ 3/2, the improved split-step theta methods can reproduce the mean-square stability of the linear test equations for any step sizes h 0. Then, under a coupled condition on the drift and diffusion coefficients, we consider exponential mean-square stability of the method for nonlinear non-autonomous stochastic differential equations. Finally, the obtained results are supported by numerical experiments.     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

Stability of equilibria of discrete-time systems in terms of invariant sets

We suggest a new approach to the verification of the stability (or asymptotic stability) of the equilibria of time-invariant discrete-time systems based on stability and asymptotic stability criteria stated in terms of invariant sets. A set-theoretic method for the verification of the conditions in these criteria is presented.     

Convergence and Mean-Square Stability of Exponential Euler Method for Semi-Linear Stochastic Delay Integro-Differential Equations

In this paper, the numerical methods for semi-linear stochastic delay integro-differential equations are studied. The uniqueness, existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with strong order $\frac{1}{2}$ and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results.     

局部资料下变分同化方法的稳定性研究

对于简化的一维扩散方程,在局部观测资料下,研究变分同化方法的稳定性.在变分同化中结合正则化方法,选择合适的正则化参数和稳定泛函,对预报模式进行修正,通过对预报精度进行先验估计,证明了该方法对于一维扩散方程的解的稳定性.修正补充相关计算结果,最后举出一个反例说明稳定性泛函的选取对于改进的变分同化方法实施的重要性.     

The asymptotic stability of the equilibrium of non-autonomous systems

A method of investigating the stability of non-linear systems acted upon by unsteady perturbations is proposed, based on the use of Lyapunov's second method. The sufficient conditions for asymptotic stability of the solutions of non-autonomous systems in critical cases are obtained.     

A new defect‐correction method for the stationary Navier‐Stokes equations based on pressure projection

A new defect‐correction method based on the pressure projection for the stationary Navier‐Stokes equations is proposed in this paper. A local stabilized technique based on the pressure projection is used in both defect step and correction step. The stability and convergence of this new method is analyzed detailedly. Finally, numerical examples confirm our theory analysis and validate high efficiency and good stability of this new method.     

计算微分代数系统稳定域的迭代Lyapunov函数方法

用迭代Lyapunov函数方法对微分代数系统稳定域进行了研究,根据所研究的微分代数系统形式,构造一个Lyapunov函数,然后对这个Lyapunov函数进行逐次迭代,给出了微分代数系统稳定域逐次扩大的迭代算法,数值实验表明迭代Lyapunov函数方法应用于微分代数系统稳定域的估计比单个Lyapunov函数具有良好的优越性。