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Each color transformation is represented by a 4 by 4 matrix, similar to matrices commonly used to transform 3D geometry.

每种颜色的转变是由一个由4矩阵，类似常用三维几何变换矩阵4。

The description of network delays including characteristics and effects are also covered and the uniformed mathematic models for NCSs with four different structures are derived. Furthermore, the controller basing on state prediction and compensating time delay is designed. Sufficient and necessary stability conditions for systems with different transmission policies such as perfect transmissions, delayed transmissions and time-varying transmissions are obtained as simple eigenvalue tests of certain test matrices. And in the end, effects of model error over maximum communication interval are analyzed. Numerical examples show the feasibility and efficiency of the proposed methods.

首先介绍了网络控制系统中数据包的传输情况以及基于模型结构方法的基本思想，并针对四种不同拓扑结构的控制网络分析了网络时延的性能，进而给出了统一的数学模型；然后，提出了基于状态预测的具有时延补偿功能的状态反馈控制器的设计方法，并针对完美传输、延时传输及时变传输三种数据传输策略，分别研究了控制系统的稳定性问题；最后分析了模型误差对最大通讯间隔的影响；仿真结果表明了设计及控制方法的正确性和有效性。

The simultaneous diagonalization by congruence of pairs of Hermitian quaternion matrices is discussed.

讨论四元数Hermitian矩阵对在共轭合同关系下的同时对角化问题。

We work out generalized Schur decomposition of quaternion matrix pencil and give out a sufficient condition for simultaneous unitary diagonalization of two quaternion matrices.

2得到了四元数矩阵束的广义Schur分解及两四元数矩阵可同时酉对角化的一个充分条件。

It is shown that finally this problem turns to the estimation of the real joint eigenvalues of three real matrices and solve the joint eigenvalue estimation by a recently proposed simultaneous diagonalization algorithm.

通过同时对角化算法估计矩阵的联合特征值，获得了参数联合估计的强可辨识性，即允许信号参数在任何一维任意重复，并可以使估计参数实现自动配对。

In this paper,from the view point of engineering realization,the problem of decentralized E-Stabilization of complex giant singular nonlinear systems is cousidered by employing the theory of variable structure contol, the property of diagonal dominant matrices and Lyapunov function.

应用变结构控制理论和对角占优矩阵的性质，结合Lyapunov函数方法，从工程实现的角度考虑并研究了一类复杂巨型广义非线性系统的分散E—镇定问题，在一定条件下。

This chapter clarifies the nested relationship between the matrix family of unitary, orthogonal, Givens, Householder, permutation, and row or column symmetric matrices. A precise correspondence of the singular values and singular vectors between the unitary-symmetric matrix and its mother matrix is derived and proved (hence a fast algorithm of singular value decomposition for unitary-symmetric matrix is straightforwardly obtained), and the corresponding perturbation bound is provided.

该章揭示了酉对称矩阵、正交对称矩阵、 Givens 对称矩阵、 Householder 对称矩阵、置换对称矩阵和行对称矩阵之间的逐级包含关系；推导并证明了，酉对称矩阵的奇异值和奇异向量与母矩阵的奇异值和奇异向量之间的定量关系，据此可得酉对称矩阵奇异值分解的快速算法；给出并证明了摄动矩阵的摄动界。

This method can find the kernel spaces of different fault distribution matrices through singular value decomposition and use it to remove the influence from residual of specified faults; a fault isolation method is given in the end.

将不同故障分布矩阵进行奇异值分解求取其核空间在分别进行故障影响消除，最后给出了故障诊断分离方法。

Upon the conditions addressed,an improved parameter-dependent l2-l∞ performance criterion is established by the introduction of a slack variable,which exhibits a kind of decoupling between Lyapunov functions and system matrices.

同时应用投影定理，通过引入附加矩阵变量，解除了系统矩阵与依赖于参数的Lyapunov函数矩阵之间的耦合，使所得到的条件更适合于滤波器的综合。

The solution for the non-stationary system is obtained through the stationary disturbed system. The gradients of the system performances to all design variables are derived and they can be used to obtain optimal solution of the systems. More generally, if the performance of the system is a function of the solution of a set of generalized Lyapunov equation, then the gradients of the performance function to the coefficient matrices of the equation can be found in closed form.

文中显示，非静态干扰系统的解可由静态干扰系统求得，而此干扰系统之最佳解，则经由本文所推导的对所有设计变数之系统性能函数梯度获得；一般而言，如果系统之性能函数是一组通式化 Lyapunov 方程式解的函数，则此方程式的系数矩阵之性能函数梯度，可用封闭解表示之。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。