矩阵函数

In this paper, the function of regression matrix is estimated in a growth curve model, and the necessary and sufficient conditions that a linear estimator of the function is admissible among the class of all lin ear estimators under matrix loss are obtained.

摘 要：对增长曲线模型中回归矩阵的函数的线性估计进行了研究。在矩阵损失下，作者得到了线性估计在一切线性估计类中可容许的充要条件。

In the thesis , firstly the problem of static output feedback H∞control was explored for discrete time singular systems. Based on the generalized Riccati inequality and linear matrix inequality, necessary and sufficient conditions were obtained for the existence of static output feedback H∞controllers, which guarantees that the resulting closed-loop system is admissible with its transfer function matrix satisfying H∞norm constraint.

本文首先利用线性矩阵不等式和广义Riccati不等式，给出离散广义系统中存在静态输出反馈H∞控制器，使得闭环系统是容许的且其传递函数矩阵满足H∞范数约束的充要条件。

A sufficient condition that ensures the stability of the origin of the system is derived, and the domain of attraction may be enlarged by applying a fuzzy anti-windup compensator to the considered system.

构造了一个更一般的Lyapunov函数—模糊Lyapunov函数来分析系统的稳定性以及估计系统的吸引域，克服了寻求一个公共的正定矩阵P的困难，使用模糊Lyapunov函数得到的系统的吸引域估计保守性更小。

Although the merit function introduced here is the sum of squares of overdetermined equations, by using the special structure of it, we successfully form the Newton equation by avoiding the product of Jacobi matrices and using only the Jacobi matrix of the function defining NCP.

对非线性互补问题，利用所构造价值函数具有的特殊非线性最小二乘结构，成功实现了具有一般意义的构造Newton方程时仅利用价值函数的一阶导数且无须计算相应残量函数Jacobi矩阵乘积的Newton法。

In Part 5, the stability of linear large-scale singular dynamic system is investigated by using the method of vector generalized Lyapunov function and the sum type of scalar generalized Lyapunov function, respectively.

首先研究线性广义系统二次型李雅普诺夫函数的存在性；然后建立按线性近似系统决定非线性广义系统稳定性的准则；进而改进广义李雅普诺夫函数法以研究广义系统的稳定性；最后提出利用非线性函数的偏导数矩阵判别非线性微分-代数系统稳定性的若干简便判据。

Adopting generalized Jordan block and algebra equivalence transform method, all of the transfer functions at different load points can be transformed to state-space description with time variable. The steady robustness of three different mode of control systems were researched by mathematic analysis. It shows that: for the high order inertia controlled object with the characteristic of nonlinear and time-variable that described by the set of transfer functions, the Luenberger function observer established according to its any algebra equivalence state-space description, if some conditions can be met, there would be a matrix of T with n′n satisfied the Sylvester matrix equation TA- FT=GC.

采用广义约当块及代数等价变换方法，可将分段的传递函数描述转换为变参数的状态空间描述，对3种典型控制系统的稳定鲁棒性所进行的理论研究表明，对同一组传递函数描述的具有非线性和时变特性的高阶惯性受控对象，依据其任一代数等价的状态空间描述所构建的Luenberger函数观测器，在满足一定的条件时，存在n′n解阵T满足Sylvester矩阵方程TA- FT=GC。

This article makes use of the approximation property of Laguerre orthogonal function series to present a Laguerre function approxima te model of linear dynamic systems.The model eliminates the need for assumption of the plant order and the time delay and approaches unknown systems via estimat ing the Laguerre coefficients on-line.

蒋中摘要：利用Laguerre正交函数序列对空间函数的良好逼近特性，建立了线性动态系统的Laguerre函数近似模型，该模型不需要对象的阶次和时延等结构知识，通过在线辨识对象的 Laguerre系数矩阵，能较好地逼近结构未知系统。

In order to solve the problem that matrix A often occurs irreversible when shape function is calculated by using traditional element free Galerkin method, the orthogonal function with the weight function is utilized in the paper. And partition of unity quadrature technique is employed and so a truly "meshless" method is realized.

针对传统无网格伽辽金方法在构造形函数时，矩阵A容易出现不可逆的弊端，采用带权正交基函数构造形函数，在积分方案上采用单位分解积分方法，从而实现了真正的"无网格"。

The second part includes the definition of positive definite function and conditional positive definite function, the basic form of Radial Basis Function interpolation, the correctness of the inversion of the interpolation matrix, the error estimate based on Kringing function.

主要包括径向基函数的相关定义，基本的插值形式，插值矩阵的可逆性，以Kringing范数为基础的径向基函数插值的局部误差估计和径向基函数插值边界附近的情况。

From theoretical analyses and calculations, it has been confirmed that the local strains around Cr〓 in SrTiO〓: Cr〓 are about twice the bulk ones. It is found that the change of Dq〓 with pressure makes main contribution to PS of ground-state g factor of SrTiO〓: Cr〓. It is the admixtures of basic wave functions that cause the strain-induced splittings of t〓E and t〓A〓 levels of SrTiO〓: Cr〓. It is found that there are non-vanishing matrix elements of operators C , C and C between wave functions with positive M〓 and those with negative M〓 and the shortcomings in previous literature have been overcome.

通过微观理论分析与计算，证实了SrTiO〓：Cr〓中Cr〓周围的局域应变大约为整体应变的两倍；阐明了基态g因子随压力的变化主要来源于Dq〓的变化；发现波函数的混合对单轴压力导致的SrTiO〓：Cr〓t〓E和t〓A〓态的分裂是至关重要的；C、C和C算符在Ms为正的波函数与M〓为负的波函数之间的矩阵元不为零，纠正了过去文献对此的错误处理。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。