In the area of estimation and filtering, performance requirements are naturally described in terms of the upper bounds on the estimation error variances of system states.

You must keep your spending within bounds.

你花钱一定要有个限度。

We're trying to keep spending within bounds.

我们尽量把花销限制在规定之内。

He bound himself to pay back the debt he owed.

他答应偿还他所欠的债。

She was under Your care and You are bound to give her back.'

我恳求，她在您的看顾之下，您会把她带回家。”

Yet the main thing to be displayed on the bookshelves were his own leather bound dairies stretching back 10 years or more.

然而，书架上的主要展品是他的皮面日记本，那些日记可以追溯到10年或更多年以前。

But I do feel duty bound to come back to contribute to the good tradition of academic debating in Oxford.

但是我觉得自己有责任回来，为延续牛津良好的学术辩论传统出一份力。

He has no money on him, he is bound to come back.

他没带钱，所以他注定会回来的。

Wrong, you're bound to come back even if you make it.

错了，就是你们成功了绝对会回来。

This paper points out that if a sequence of Jacobian approximation satisfies the bounded deterioration, the sequence generated from the quasi& Newton methods is no better than linear convergence.

本文指出当Jacobian近似满足有界退化性质时，由拟牛顿算法得到的迭代序列最多是线性收敛的。

For a nonlinear system of ordinary differential equations, we construct an iterative sequence and prove that the sequence is bounded. Using the sequence, the approximate solution is obtained.

对于非线性微分方程组，构造了一个迭代序列，证明了迭代序列是有界的，利用迭代序列构造近似解的表达形式。

The ∧-bounded variation functions on sequence spaces

叙列空间上的∧&有界变差函数

The bounded variation sequence is applied broadly.

囿变数列又称为有界变差数列，在函数论中有广泛的应用。

Notes on the Bounded Variation Sequence and Its Characteristic

关于囿变数列及其特征的若干注记

Based on the view that the theorem of closed mested interval is an axiom, this paper deduces the essential limit of monotonic bounded sequence of number and the Dedekind theorem, and proves the general theorem of bull closed nested interval of real number.

以通常所说的闭区间套定理作为公理推出单调有界数列存在极限和Dedekind定理，并且证明了通常所说的实数满闭区间套定理。

Bounded Property of Infinite Matrix Transformation Set about Echelon Space

关于Echelon空间无穷矩阵变换集的有界性

The existence conditions and definition region of a grey inverse matrix are studied. Additionally, the new concept of grey rank of a bounded grey matrix and its algorithm are proposed and the criteria for constant-full-rank, constant-non-full-rank, conditional-full-rank of a bounded grey matrix are given.

此外，本文又提出有界灰矩阵的灰秩的新概念与算法，建立了有界灰矩阵恒满秩、恒不满秩、条件满秩的判据。

The nonsingularity and rank of a bounded grey matrix

有界灰矩阵的非奇异性与秩

Research on the Stability of Bounded Grey Matrix

有界灰阵稳定性的研究

Based on the Lyapunov stable theory, a linear state feedback controller is presented to guarantee the asymptotic stability and achieve the bounded state variable for any bounded disturbance.

基于Lyapunov稳定性理论，设计了一个线性状态反馈控制器，该控制器对于任何给定的有界干扰，都能保证系统渐近稳定并获得有界的状态变量。

The optimal inputs are given by the state feedback with the bounded variable gains.

最优输入由有界可变增益的状态反馈得到。