系统函数

In this paper we present a converse Lyapunov theorem for globally uniform asymptotically controllably switched systems.And we consider general nonlinear switched systems.

本文对一类全局一致渐进能控的非线性切换系统的控制Lyapunov函数的存在性进行了研究，证明了一个非线性切换控制系统如果是一致全局渐进能控的，那么存在一个公共的控制Lyapunov函数。

Based on the analysis of models proposed, the cumulative distribution functions and probability density functions of strength of systems were derived respectively.

在研究系统可靠性模型的基础上，建立了系统强度的累积分布函数和概率密度函数。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

The distribution function of the system response and state function is approximately determined by the standard normal distribution functions using Edgeworth series, and its reliability is obtained.

在结构系统响应和状态函数的前四阶矩的一般数学表达式的基础上，使用 Edgeworth级数把未知响应和状态函数的概率分布展开成标准的正态分布表达式，并放松了对随机参数的分布概型和激励类型的限制，从而确定了系统的可靠度

The solution of the equation and the period of the particle motion for a non-pertubated system are expressed exactly by means of Jacobian elliptic function and the 1-st kind elliptic integral.Melnikov function of the rotated periodic orbit is constructed,and also bifurcation of the system is analyzed by the method.

利用Jacobian椭圆函数和椭圆积分给出了系统的解和粒子运动周期，用Melnikov方法构造了旋转型周期轨道的Melnikov函数，并用这个方法分析了系统的局部分叉性质。

The first one is an algorithm with terminal sliding mode equality constraint. The second is a dual-mode control scheme, which enlarge the terminal region. The sliding mode based MPC is implemented while system state is outside of terminal region, and sliding mode variable structure control designed off-line is used once system state arrives in the terminal region.

第一种方法为终端滑模等式约束非线性模型预测控制方法，首先离线设计切换函数使得滑动模态渐近稳定，然后在有限预测时域的基础上对切换函数附加一个终端等式约束；第二种方法为双模控制方案，在终端区外采用模型预测控制，使得系统状态在有限时域内到达终端区内；在终端区内部采用离线设计的滑模变结构控制，使得系统渐近稳定。

According to Oseledec multiplicative ergodic theory and singular boundary theory, the conditions of local and global stability were acquired.

为了研究随机因素对经济系统稳定性的影响，建立了系统可靠性函数和首次穿越时间概率密度函数，并结合初始条件和边界条件得到了数值结果。

Based on the normative fractional Fourier transform and the concept of the optical transfer function, using the linear system theory, the mathematic expressions of fractional transfer function in Fresnel diffraction system and Fraunhofer diffraction system are given respectively.

基于规范光学分数傅里叶变换，从光学传递函数概念出发，根据菲涅耳衍射、夫琅和费衍射定义，应用线性系统理论，分别给出了菲涅耳与夫琅和费衍射系统在规范分数傅里叶变换下的光学传递函数数学表达式。

One position control system is introduced as the objective controlled by FOC. Based on Mittag-Leffler function, the fractional order control system with full memory length is adopted as evaluation criterion, and an approximation performance function of discretization methods is proposed. Analyzing the time domain error and approximation performance, the investigation to various discretization methods is carried out comparatively in detail.

引入一个位置控制系统作为分数阶控制对象，将Mittag-Leffler函数的全记忆长度分数阶控制系统作为评估基准，提出了一种离散算法的近似性能函数，通过时域误差分析以及近似性能分析，对比研究了分数阶微积分算子的数字实现方法。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷