矩阵范数

By means of generalized Lyapunov function and linear matrix inequality,the asymptotical stability with zero solution is studied for the system,and a sufficient condition is given such that the system is asymptotically stable with zero solution and also a H∞ norm constraint .

针对非线性离散广义系统研究了状态反馈H∞控制器的设计问题，利用广义Lyapunov函数和线性矩阵不等式，首先对系统的零解渐近稳定问题进行了研究，并在此基础上给出了系统的零解渐近稳定且具有H∞范数约束的充分条件，之后设计了状态反馈H∞控制器，使闭环系统具有同样的性能，最后给出了数值算例说明本文结论的有效性和可行性

Where the uncertain matrix is norm bounded and time-varying , while the external disturbance is a stochastic process.

假设不确定参数矩阵是时变，范数有界的，外部干扰是一个随机过程。

The controller makes the closed-loop systems internally stable and minimizes the H2 norm of the transfer matrix Tzw from w to z. Two Riccati formulae based on 8 operator is deduced. The H2 problems for continuous time systems, Z operator models and 8 operator models are investigated respectively.The guaranteed cost control problem of robust stabilization and robust performance for uncertain systems which is described by 8 operator is discussed in this paper.

采用Riccati方程处理方法讨论了基于Delta算子描述下的离散系统存在输出反馈控制器的问题，得到了两个基于Delta算子的Riccati方程，设计了Delta域的输出反馈控制器，使得闭环系统内稳定，且满足从w到z的传递矩阵T_的H_2范数最小，设计了基于Delta算子描述下的离散系统的最优控制器，并与S域和Z域的H_2控制器进行了比较。

Robust stability criteria, the design methods of robust stabilizing controller and guaranteeing certain robust performance controller for linear time-delay system with norm-bounded uncertainties or convex polyhedron uncertainties are studied in this paper by delay independent method and delay dependent method.

针对具有范数有界不确定参数和凸多面体不确定参数的线性不确定时滞系统，分别给出了它们时滞无关指定鲁棒H~∞性能约束可镇定的充分必要条件以及相应的控制器设计方法，结果以线性矩阵不等式的n浙江大学博士学位论文形式给出。

In the presence of impulsive noise,the two received signals are combinated,so the estimated impulse response of the channel is the eigenvector of its covariation matrix corresponding to the smallest eigenvalue,which can be realized adaptively using generalization o.

该算法在脉冲噪声环境下，组合两个接收信号，使其共变矩阵最小特征值对应的特征向量为信道的估计，并基于广义归一化最小平均p范数方法自适应得到该特征向量，从而获得时延估计。

GPS (Geometrical product specification and verification); database; general ; GPS matrix model; duality principle; LSC; norm theory

工程科技II，工业通用技术及设备，工业通用技术与设备GPS；数据库；通用； GPS；矩阵模型；对偶性原理；最小二乘法；范数

In this part we use the linear matrix inequation method.

第三，针对范数有界不确定性，采用线性矩阵不等式方法，利用输出反馈来镇定系统。

In chapter 2 we make perturbation analysis for the two kinds of nonsingular systems AX=B and systems with multiple right hands involving Kronecker product, and derive normwise , mixed and componentwise condition numbers and their upper bounds respectively.

在第二章中我们对两类非奇异线性方程组AX=B和带Kronecker积的多右端系统进行了扰动分析，并应用矩阵导数得到范数型，混合型和分量型这三种条件数及其上界。

By applying these two tools,we mainly discuss the problems as follows:1 Perturbation identities for the generalized polar decomposition:By applying singular value decomposition, we study the perturbation bounds of the generalized polar decomposition under unitary invariant norms when A is perturbed by addition or multiplication,respectively and give our bounds in identities.2 A class of new unitary invariant metrics: This paper generalized a class of new unitarily invariant metrics and give the upper-bounds and lower-bounds by C-S decomposition.

利用这两个强有力的工具，本文主要讨论了如下问题：1 矩阵广义极分解的扰动等式：利用奇异值分解，本文分别讨论了加法扰动和乘法扰动下矩阵广义极分解在任意酉不变范数下的扰动界，并首次以恒等式的形式给出了酉极因子和半正定因子的扰动界。2 一类新的酉不变度量：本文推广了文[22] 中的结论，定义了一类新的酉不变度量。

An on-line blind source separation algorithm of non-stationary mixed signals is presented. The algorithm uses the multiple time-delayed decorrelation and natural gradient rule to obtain the stationary point of the cost function, only a small number of observed samples is needed to minimize the Frobenius norm of the correlation matrices, so the computing cost is low and continuous separation calculation could be realized by on-line operation.

利用一种基于多时延解相关准则的代价函数和自然梯度原则，分别推导出非平稳信号在瞬态线性混合及卷积混合情况下的在线盲分离算法，仅通过对有限个时延样本的相关矩阵进行Frobenius范数最小化运算得到分离矩阵，计算工作量小，无需对样本进行分块处理，可实现对信号的连续跟踪操作。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。