线性的

Secondly, the problem of observer design for Lipschitz switched nonlinear systems is considered. By proposing a proper switching strategy and utilizing Schur complement formula and the related notion of LMI, we design a quadratically stable observer which can be used for both finite and infinite switched nonlinear systems. The main result is given in the form of linear matrix inequality. Simulations validate the correctness of the presented algorithms. The simplicity of the design algorithm makes it easy to be carried out.

通过设计适当的切换策略，利用Schur补公式和线性矩阵不等式的相关知识，给出了一种全局二次稳定的观测器的设计方案，这种方案适用于有限和无限切换系统，主要结果以线性矩阵不等式的形式给出，通过仿真实例验证了所提方案的正确有效性，该部分设计思路简单、易实现。

In the chapter three, by using the comparison principle and frequency domain method of the discrete systems with time-delay, combining Rouche Theorem, sufficient criterions for the stabilization of the neutral type discrete control systems with multiple time-delay and the neutral type interval coefficient discrete control systems with multiple time-delay are obtained by choosing appropriate feedback controller.

在第三章，利用时滞离散系统的比较原理与时域法，结合复变函数理论中的路歇定理，通过选取适当的反馈控制律，得到了多组时滞中立型线性定常离散控制系统和多组时滞中立型区间系数线性定常离散控制系统的无条件镇定的充分性准则。

The existence theorem of generalized weak efficient solutions with respect to variable, cone for a linear G〓teaux differentiable mapping is proved with set valued mapping fixed-point theorem and the relation between a vector optimization and a variational inequality problem. The existence of weak efficient solutions for multi-objective convex vector optimization is characterized.

建立映射在线性G〓teaux可微条件下关于可变锥的广义弱有效解的存在性及多目标凸向量优化问题在G〓teaux可微条件下弱有效解的特征，利用集值映射不动点定理及向量优化与变分不等式的关系证明线性G〓teaux可微锥凸映射关于可变锥的广义弱有效解的存在性定理。

The conditional nonlinear optimal perturbation is a new theoretical method proposed by Mu,et al in 2003, which is an extension of the linear singular vector to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system.

条件非线性最优扰动是Mu等2003年提出的一个新的理论方法，它是线性奇异向量在非线性情形的推广，克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷，成为非线性系统可预报性和敏感性等研究新的有效工具。

The conditional nonlinear optimal perturbation is a new theoretical method proposed by Mu , et al in 2003, which is an extension of the linear singular vector to nonlinear regimes. It has become a powerful tool to study some issues of nonlinear systems like predictability, sensitivity and so on, because it overcomes the defect of LSV for not representing the fastest developing perturbation of a nonlinear system.

摘要条件非线性最优扰动是 Mu 等2003年提出的一个新的理论方法，它是线性奇异向量在非线性情形的推广，克服了线性奇异向量不能代表非线性系统最快发展扰动的缺陷，成为非线性系统可预报性和敏感性等研究新的有效工具。

With this method, we had several important differences compared to the YDmodel. First, the ratio of daily increment of PDT and the deficit of both water and nitrogen was used to estimate the effect of environment. Second, a nonlinear function was adopted to describe vernalization and thermal effectiveness (instead of three-stage linear function). Third, sinusoidal function was used to describe photoperiod curve cluster for different cultivars.

本模型在YDmodel基础上的改进主要有3点：（1）将每日生理发育时间的增量乘以水肥丰缺因子，改为除以水肥丰缺因子表现水肥对大麦发育的影响，客观体现了大麦在水肥丰缺条件下的发育延迟或提早现象；（2）将三段线性函数改为非线性函数表达春化效应和相对热效应，确立了不同品种相对春化效应和相对热效应的曲线族；（3）将线性函数改为正弦函数表达不同品种光周期效应。

Experimental result showed that under the wavelength of 460 nm,there was good linear relation between absorbency and content of SO42-;and stationary time that absorbency value needed became longer along with the increase of sample quantity of phosphoric acid.When absorbency become stationary,there is good linear relation between the phosphoric acid sample quantity and the content ofSO42-.So the content of SO42- can be adjusted by turning the sample quantity to make it in scope of standard curve.

实验结果表明，在波长为460 nm处，硫酸根含量与吸光度成良好的线性关系；随着磷酸取样量的增加，吸光度达到稳定值所需的时间相应增加，稳定后磷酸取样量与硫酸根含量成良好线性关系，因此实验过程中可通过调整磷酸的取样量来调节硫酸根含量，使之在标准曲线的测定范围内。

Be based on these conditions, construction gives strict linear matrix inequality , filling property proved the Schur that uses matrix next to be below the condition of linear matrix inequality, system of earning closed circuit is asymptotic stability, specific condition feedback gave out to control a law in the meantime.

基于这些条件，构造出严格的线性矩阵不等式，然后利用矩阵的Schur补性质论证了在线性矩阵不等式的条件下，所得闭环系统是渐近稳定的，同时给出了具体的状态反馈控制律。

The theoretical analysis are verified by numerical simulations.Chapter 3 mainly considers a class of predator-prey model with sublinear functional response function. We deduce some sufficient conditions ensuring stability of equilibrium, nonexistence , existence as well as uniqueness of the limit cycle around the positive equilibrium.

第3章研究了一类食饵为线性密度制约，功能反应函数为次线性函数的食饵-捕食者模型，完整地对模型的平衡点的全局稳定性和极限环的存在惟一性进行了定性分析，得到了该系统不存在闭轨线，正平衡点全局稳定和存在惟一稳定的极限环的充分条件。

With the development of lasers and synthesization of novel nonlinearoptical materials, people begin to study on nonlinear optics, especiallymulti-photon process.

随着激光器的发展，新型非线性光学材料的合成，人们的研究方向不再拘泥于简单的线性光学，而更多的是非线性光学。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新