积分不等式论文参考文献

先介绍定积分的历史背景！然后综合你的参考文献，说下你的文献里的研究现状！然后，你说下你发现这些文献少了些什么（比如，针对性不够，不够系统等等）然后，你就说你要在这些文献的基础上，做出什么样的研究（比如，你要用某某方法证明“定积分不等式”，当然，不一定要你的证明是最好的！但你一定要保证，这种证法是前所未有，同时，你还要举事例说明你的证法的应用方面的优越性）

1.The existence of time delay would deteriorate the performance of system or even be the important source of instability.     时滞的存在可能会破坏系统性能，甚至造成不稳定 2.Time delays are frequently encountered in many fields of science and engineering, and they are often a source of degradation in system performance or instability.     时滞现象频繁出现在许多科学和工程的领域中，并且它通常是导致系统性能下降或不稳定的原因。     3. In both delayed control and delayed measurement, the delay is usually considered undesirable since it has the tendency to deteriorate the system performance or even destabilize the system.     在具有延时的控制和测量中，时滞是不受待见的，因为它具有使系统性能恶化甚至使系统不稳定的趋势。 4. The last decade has shown an increasing research activity on time-delay and/or sampled-data systems analysis and control due to both emerging adapted theoretical tools and also practical issues in the engineering field and information technology (see Sipahi, Niculescu, Abdallah, Michiels, and Gu (2011) and Zhang, Branicky, and Phillips (2001) and references therein).     在过去的十年中，由于出现了新的适应性理论工具以及工程领域和信息技术领域的实际问题，因此在时延和/或采样数据系统分析和控制方面的研究活动不断增加（请参见Sipahi，Niculescu，Abdallah，Michiels ，以及Gu（2011）和Zhang，Branicky和Phillips（2001）以及其中的参考文献）。 5.Recently, there has been rapidly growing interest in the stability of the system with time-varying delays, which has strong background in engineering field , such as a networked control system, see  for example [1,2]. 最近，时滞系统的稳定性问题引起了广泛的关注，这在工程领域有很强的背景，如网络控制系统 6.The derived delay-dependent criteria based on the LKF approach are usually expressed in forms of linear matrix inequalities (LMIs), whose conservatism is often judged by the upper bound of the time-varying delay.1.The method of Lyapunov-Krasovskii function (LKF) is one of the most popular approaches. In LKF, some useful terms are not ignored but considered, which makes the result much less conservative.     LF泛函方法是重要的方法。考虑一些被忽略的项，能够降低保守性1. Delays can cause oscillations or bad performance in a system. This makes it necessary to study stability of time-delayed systems. In addition to stability, for some applications, it may be crucial to determine the convergence rate or the transient decaying rate of system states.     时滞会产生差的系统性能。研究时滞系统是必要的。除了稳定性以外，对于某些应用而言，确定系统状态的收敛速率或瞬态衰减速率可能至关重要。 1. Cross-coupling control idea is widely used to design the synchronization  controller,  which  can  be  seen  in literatures[2–8,11,13–17,20,22].     交叉控制思想已经广泛被用于设计同步控制器，如文献[2-8] 2. Steel rolling mill control  is an example of measurement delay, which is found in Sbarbaro-Hofer [240].     轧机控制是测量延迟的一个例子，可以在Sbarbaro Hofer[240]中找到。 3. Analysis of the delayed resonator  as well as  its applications  are reported  in [216, 217, 63, 125].     [216，217，63，125]对延迟谐振器及其应用进行了的分析。 4. For example, the finite dimensional systems could represent a dynamic controller for a system modeled by a PDE ( see d’Andréa Novel, Boustany, Conrad, and Rao (1994), Krstic (2009) and references therein ).     例如，有限维系统可以代表由PDE建模的系统的动态控制器（请参见d'AndréaNovel，Boustany，Conrad和Rao（1994），Krstic（2009）及其参考）。 5. Instead , a system of ordinary differential equations (ODEs) can model a component coupled to a phenomenon described by PDEs as in Daafouz, Tucsnak, and Valein (2014).     相反，如Daafouz，Tucsnak和Valein（2014）所述，常微分方程组（ODE）可以对与PDE描述的现象耦合的组件进行建模。 6. In the past few decades, fruitful results have been obtained for the robust stability of uncertain systems with time-varying delays by using the LKF approach.     过去几十年，时滞不确定系统的鲁棒稳定性已经取得丰硕研究成果，通过使用LKF方法 7.The core idea behind an event-triggered control is that the update of control commands is only executed after the occurrence of an event rather than the lapse of time in a periodic fashion注意：介绍具体的现有研究工作，不是简单的堆叠，需要有层次，逻辑，目的。简单的说，要通过现有的结果，凸显出研究的必要性和重要性。基本上可以采取总—分—总的结构，     总：研究的主要方向，思路，方法     分：针对不同的方向，列举参考文献；注意不应随意列举，要有代表性，并且对文章有所点评，指出不足或优点。这部分的目的仍然是要突出             自己文章的优越性。     总：综上所述，本文研究的目的是为了解决现有文献中的哪些不足 1. The time domain method based on Lyapunov stability theory is abroad exploited . Among some inequality-based stability conditions, the linear matrix inequality (LMI) approach becomes a powerful and popular means to tackle the stability issues of power systems with  time-varying delays (see [4], [6], and [9]–[12]).     基于Lyapunov稳定理论的时域方法广泛研究。一些基于不等式的稳定性条件中，线性矩阵不等式的方法是解决具有时变时滞电力系统稳定问题的有效工具 2. To handle the time-varying and random delays, the time domain indirect methods based on Lyapunov stability theory and linear matrix inequality techniques (LMIs) have been proposed as an effective method to obtain approximate value of the delay margin [13].     为了处理时变时滞和随机时滞，基于Lyapunov稳定理论的时域直接方法和线性矩阵不等式技术已经成为获得时滞裕度近似值的一个有效方法 3. In order to diminish the conservatism for the stability conditions of time-varying delay systems, many approaches were developed. The main efforts have been focused on two aspects: one is the techniques of constructing L–K functional , such as delay-division functional, functional with matrices dependent on the time delays [13], functional including the ones with triple-integral terms [14], and quadratic terms which is multiplied by a higher degree scalar function [15] .The other is the analyzing methods for estimating the derivatives of L–K functionals with respect to time , such as improved majorization technique, free weighting matrix method [16], integral inequality including Jensen inequality [11], Wirtinger inequality [17], auxiliary function-based integral inequality [18],  and convex combination ideas incorporating linear convex analysis [19], reciprocal convex technique [20], and quadratic convex approach [21].     许多方法被用来减少时变时滞系统稳定判据的保守性。主要工作集中在两个方面：一是L-K泛函的构建，如：时滞分割函数，其函数矩阵决于时滞[13]，具有三重积分项的函数[14]，和高阶标量函数相乘的二次项[15]。另一方面是估计L-K泛函时间导数的分析方法，如：改进的专业化技术，自由加权矩阵方法[16]，Jensen不等式[11]，Wirtinger不等式[17]，基于辅助函数的积分不等式[18]以及结合线性凸分析的凸组合思想[19] ，倒凸技术[20]和二次凸方法[21]。 4. The last decade has seen a tremendous emergence of research devoted to the construction of Lyapunov–Krasovskii functionals which aims at reducing the inherent conservatism of this approach.     过去10年中，大量研究致力于构造L-K泛函，旨在减少固有保守性 4.1 Apart the choice of the functional, an important source of conservatism relies also on the way to bound some cross terms arisen when manipulating the derivative of the Lyapunov–Krasovskii functional.     除了泛函的选择，保守性的另一个来源是处理L-K泛函导数时产生的交叉项 1. Zhang et al. [1] have developed chaotic speed synchronization controller for multiple induction motors by using stator flux regulation. xx[1] 利用 定子磁通量调节技术 开发 了 用于 多个感应电动机的混沌速度同步控制器。 2. Starting from a semi-group modeling of the PDEs, the authors of Gahlawat and Peet (2017) construct a very general Lyapunov functional whose parameters are optimized via a sum of square procedure ( see also Ahmadi, Valmorbida, & Papachristodoulou, 2016).     起始于PDEs的半群模型，(2017)中的作者构建了一个非常一般化的Lyapunov 泛函，其参数通过平方和流程优化 1. In combination with a simple choice of Lyapunov–Krasovskii functionals, this inequality leads to new stability criteria for linear time-delay and sampled-data systems.     结合简单选择的Lyapunov–Krasovskii函数，这种不等式能够得到线性时滞和采样数据系统的新稳定性标准。1. 在现有文献中      reported in the literature 2. 近年来/多年        in the last decade  3.研究结果被推广  The result of this study can be generalized for …   4. 本文旨在讨论      It is the aim(intend, purpose) of this paper to discuss (present, describe)    5. 已经得到             have concluded, gained, obtained, yielded, arrived at, generated, acquired, achieved 6. 结果表明             This result(fact, demonstration, illustration, classification, comparison, analyses) gives (shows)  7.公式是基于          The formulas is derived for … according to … 1. Do not hesitate to contact me if I can be of any assistance.