范数

By introducing a differential-difference adaptive law, an adaptive repetitive learning control strategy is designed to ensure the asymptotic convergence of the extended tracking error in the sense of square error norm.

通过引进微分－差分参数自适应律，设计了一种自适应控制策略，使广义跟踪误差在误差平方范数意义下渐近收敛于零。

A differential-difference mixed-type adaptive law and an adaptive learning control method are constructed to ensure the asymptotic convergence of the extended tracking error in the sense of square error norm.

通过引进新颖的微分－差分混合型参数自适应律，使广义跟踪误差在误差平方范数意义下渐近收敛于零。

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

The asymptoticbehavior of two ecological systems and the unconditionally stability and oscillations in kinds of 4-order delay difference equations are investigated by using analysis method, constructing Lyapunovfunctions, the logarithmic norm, charateristic roots theory and the bifurcation theory. Here, theasymptotic properity includes the uniform persistence, the global attractability of the solutions,the asymptotic stability of the positive solution local or global and the oscillations of solutions.

本文利用定性分析的方法、比较原理、特征值分析法、对数范数、构造Lyapunov函数及分支理论等方法和理论，研究了两类生态模型解的渐近性及一类四阶时滞微分方程解的无条件稳定性，其中包含模型的一致持久生存性、正平衡态的全局吸引性、局部和全局渐近性以及解的振动性等问题。

By means of analyzing the noise error, it is proposed to use an algorithm of singular value decomposition total least squares to conduct the interharmonics estimation, namely taking the noise interference at both sides of the matrix equation into account simultaneously and solving the minimum norm problem by least square method under such condition. In the proposed algorithm by means of singular value decomposition of a new augmented matrix and by use of a simple and practical method to determine the number of principal singular value related to signal to noise ratio, the storage calculation of right singular matrix is performed, thus a more accurate frequency estimation of interharmonics can be obtained.

通过分析噪声误差，提出采用奇异值总体最小二乘(singular value decomposition total least squares，SVDTLS)算法进行间谐波频率估计，即同时考虑矩阵方程两边的噪声干扰，采用SVDTLS算法求解该情况下的最小范数解，通过对增广矩阵进行奇异值分解(singular value decomposition，SVD)，采用简单实用的与信噪比相关的主奇异值个数确定方法对分解的右奇异矩阵进行存储计算，得到了较精确的间谐波频率估计结果。

It is a global convergence method, so it can avoid the drawback of the Newton method. The main idea is to perturb the TV-norm functional term of the Euler-Lagrange equation so large that it can be solved by the Newton method when the observed image is an initial value, and we regard this equation as an auxiliary equation.

它的主要思想是将Euler-Lagrange方程中TV-范数做一个足够大的扰动，得到一个能用以观测图像z为初值的牛顿法求解的辅助方程，通过构造同伦方程将辅助方程和Euler-Lagrange方程联系起来。

For every step of arbitrary m-th order finite element methods of nonlinear Hamiltonian systems are first proved high accuracy conservate their symplectic structure, through construct a new auxiliary equation and negative norm estimated of error.

对非线性Hamilton系统的任意m次有限元法，构造了新的辅助问题，并得到误差估计和负范数估计，首次证明m次有限元对每一次步进是高精度Oh~(2m+1意义下近似保辛的。

The uncertainty is assumed to be unknown continuous function with norm-bounded restriction. The perturbation is sector-bounded.

系统的不确定性是范数有界的未知连续函数，外部干扰是扇形有界的。

Thus there has been an increased interest in studying theexistence and multiplicity of periodic boundary value problem.

因而受到人们广泛的关注，发展和解决这类问题的一些有效的方法如Lyapunov泛函方法，不动点和范数形式的锥拉伸锥压缩不动点定理等。

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。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。