查询词典 sufficient condition

In this paper, one sufficient condition for the global asymptotical stability of the three-dimensional cooperative system is derived using the nonpositive divergence and the properties of monotone flow.

利用非负散度和单调流性质推导出三维合作系统全局渐近稳定的充分条件，并将该条件应用到一些具体的三维合作系统系统的稳定性判定中，所得结果说明了Hirsch所提出的猜测的正确性，同时推广和改进了相关文献的已有研究成果。

The necessary and sufficient condition for that the problem P〓 is nonsingular is derived.

利用原问题与P〓的等价性，给出了原系统二次指标最优控制器的设计，保证了闭环对给定的初值有唯一的光滑轨线且零解渐近稳定。

A important result is the one-order expression of AR Yt = DYt-1 + E, from paralleling a high-order differential equation transformation into a one-order differential equation system, the one-order expression exposes that the AR is only a certain more-multivariable power series processAnd, if a process is described as an AR, the sufficient and necessary condition is the spectrum norm A of the coefficient matrix D less than one.

作者用高阶微分方程化一阶微分方程组的方法，获得多元弱平稳序列p阶自回归模型的一步滑动平均表达式，证明了AR的是一个更高维的幂级数的线性过程，从而，说明了AR关于序列依概率成立的充要条件是：该模型更高维的幂级数的线性过程的表达式中系数矩阵D的谱范数λ＜1。

The satisfiability of conjunction normal form is a typical NP-complete problem. To study the complexity of SAT problem, a new concept of saturated clause muster has been introduced with using the characteristic of saturated clause muster. The sufficient condition of SAT problem was approved to be a polynomial and has opened out essential distinction of 2SAT and 3SAT problems.

合取范式可满足性问题是典型的NP完全问题，本文引入了一个饱和子句集的新概念，利用饱和子句集的特性，研究了SAT问题的复杂性，证明了SAT问题复杂性为多项式的一个充分条件，并揭示了二元可满足性问题与三元可满足性问题的本质差别。

In the second chapter, we obtain a sufficient condition for that there exist two elements x and y which satisfy x⊥Iyand x⊥By. As a result, it is proved that there exist elements x and y with x⊥Iyand x⊥Eyin any real two-dimensional normed linear space.

本文从点态入手，在第二章中，给出了既等腰正交又Birkhoff正交的元存在的一个充分条件，证明了在任意实二维赋范线性空间中既等腰正交又欧式正交的元的存在性。

The error growth of numerical method grows linearly with the stage of iterated matrix. A sufficient condition of bounded stability for linear θ-method is proved.

证明了数值方法的计算误差是随着迭代矩阵的级数线性增长的，又进一步给出了线性θ-方法有界稳定的一个充分条件。

The problem of PI controller design for the multi-input and multi-output system is transformed to that of static output feedback controller design via the new state variable. As to the problem of the static output feedback, a new LMI-based sufficient condition of the controller is presented in this thesis. We can gain the multivariable PI controllers just solving one LMI inequality. The numerical example is provided to illustrate the proposed design approach. 3.The H_∞ robust control is able to solve the multivariable problem, also the control problem characteristic of the modeling error, parameters uncertainties and unknown perturbation, Its application research in the power electronics is beginning now. Considering the characteristics of the PWM DC-DC converters, a multivariable PI controllers which is based on H_∞ Performance Index is designed.

通过构造新的状态变量，可以将多输入多输出系统的PI控制器设计问题转化为静态输出反馈控制问题，利用后者的成熟理论来设计控制器；本文在问题转化后采用更为简便的算法，只需通过求解一个LMI不等式，就能求取基于H_∞性能指标的多变量PI控制器参数，实例验证了算法的有效性。3.H_∞鲁棒控制具有处理多变量问题的能力，可解决具有建模误差、参数不确定和干扰未知系统的控制问题；它在电力电子学中的应用研究刚刚开始。

In Chapter four, the stability problem of the nonlinear open-loop control system is discussed by the concept of input-output stability. The L〓 stability is defined, the relationship between the L〓 norm of output variable and the input variable is proven firstly, and the sufficient condition for the stability of open-loop system , the H〓 norm of the n-th order frequency response function decreasing by n!

本章给出了非线性控制系统L〓稳定性的定义，首次严格证明了输出变量的L〓范数与输入变量的L〓范数之间的一个重要的关系式，并得到了一个开环系统L〓稳定性的充分条件，即n阶广义频率响应函数的范数〓应按n！

The finite-gain stability of the controller was proved under the assumption that the kernel function was local Lipschitz in this open-loop inverse control system. The sufficient condition for that Gaussian kernel function to the local Lipschitz of either variable was given. The stability of the whole system was also proved under some proper assumptions.

针对此开环逆控制系统，在核函数为局部Lipschitz的前提下，证明了控制器是有限增益稳定的，并给出Gaussian核函数对任一变量的局部Lipschitz性的充分条件，在一定合理的假设下给出了控制系统的稳定性结论。

Secondly, we investigate C°-flows on orientable closed surfaces having POTP, and obtain a necessary and sufficient condition of such flows.

剖析了这些轨道的邻域的轨线结构，还考虑了经过Poisson稳定点及几乎周期点的横截圈和相应的回归映射，其中本文讨论了可定向闭曲面上具有伪轨跟踪性质的C〓-流，得到了可定向闭曲面上C〓-流具有伪轨跟踪性质的较为简洁的充分必要条件；最后本文借助于从可定向的闭曲面到不可定向闭曲面的复叠投射，讨论了不可定向闭曲面上的C〓-流与其提升的轨线之间的联系，解决了不可定向闭曲面上C〓-流具有伪轨跟踪性质的判定问题。

Warden: That's a beautiful dog, but don't bring her again.

那是条漂亮的狗，但是不要再把她带来了。

You get up in the morning – no hangover!

你第二天早上起来的时候—不会宿醉！