工程中时延动态系统的定量稳定性分析
摘要
工程中的通常概念可以看成信息的操作。策划和执行是两个重要的信息操作过程，前者是信息的研究，而后者是所获信息的有效利用，以便达到预定目标的过程。同时，目标和逼近是信息执行的不可缺少的组成部分。因此，本文第一个贡献如下所述。
(a)从信息的观点，给出控制、时延相关稳定判据和时延不相关稳定判据的概念描述。提出神经网络的函数逼近定义。从数学描述上看，神经网络应用应以所要研究的对象特性为出发点。所以，作者认为神经网络的定义也应与相应的目标函数密切相关。对于相同的非线性对象，神经网络的不同会影响应用的效果和神经网络本身的复杂性。
实际中，存在于通讯设备和实际系统本身的时延扰动无处不在，并且通常被认为是一个重要的不稳定因素。因此，研究时延系统的特性，有着重要的意义。而且，在研究系统的稳定性过程中，专家们不但想得到关于稳定性的定性描述，更希望得到关于实际系统解的过渡过程的定量信息。所以，许多年来，定量稳定性研究一直得到广泛关注。本文在这方面的研究成果与其他学者贡献的区别在于以下几点：
(b)关于数字电路中连接线的块状参数梯形网络模型，给出迄今为止最紧的全局开关延迟时间的估计界限。
(c)基于两类假设，开创性地研究两类Razumikhin型泛函微分方程(FDE)解的衰变估计。所研究的这些FDE在许多研究成果中发挥着重要作用。从Razumikhin定理的应用角度出发，相关文献中的众多结果可以得到相应的拓广。
(d)对于在实际时延系统的稳定性分析的过程中经常遇到，并且成为关键问题的一类标量时变时延微分不等式，创造性地构造出其解的稳定性的定量描述形式。
(e)首次提出带有输入时延扰动的LQ调节器和静态输出反馈控制器的时延相关定量稳定性判据。
(f)创造性地导出具有时变时延扰动的神经动态系统的全局时延不相关定量稳定性判据。扩展这方面关于时延不相关稳定性研究的已知结果，并且给出神经网络状态轨迹的衰变估计。
(g)研究检验带有扰动的滞后型泛函微分方程(RFDE)正不变集的条件，并且首次引入带有非线性输入时延扰动的线性系统状态的正不变集概念，给出这类系统状态的非对称正不变集检验的充分条件。
本文的总体结构安排如下：
(a)在第一章中，对一个富有挑战性的课题一时延系统的主要进展和发展趋势进行系统地综述，引入控制、神经网络和稳定性概念。
(b)正象以前的研究成果所指出的那样，电子电路中连接线上时延的研究，具有基础的重要性。在本文第二章，以电路分析中通常采用的带有电容负载的n
General conceptions in engineering can be viewed as the operation of the information. Plan and action are two important conceptions in the procedure to operate information. The first is to investigate the information while the other is to employ the obtained information to achieve the motivation efficiently. The action with respect to information consists of the motivation and the approximation. So, I think the first reasonable contribution in this work is stated as follows.
(a) The basic conceptions, such as control, delay-dependent stability criteria, and delay-independent stability criteria, are defined from the point of information. In the light of the function approximation approach, the definition of general neural networks is presented. From the description of mathematics, applications of neural networks should be based on the investigations of the practical systems. Hence, the author think that the definition of neural networks is related to the functions to be modeled. The performance of systems and the complexities of neural networks are adjustable as different neural networks are applied to the same plant.
Time delay perturbations, which exist in communication equipment and plants, are ubiquitous and generally regarded as sources of instability in the practical engineering. So, it is of important to study the performance of retarded engineering systems. Moreover, in the procedure of stability analysis, experts are not only interested in the stability properties, but also in quantitative transient characteristics of solutions of systems. Therefore, the investigation on the quantitative stability has reasonably attracted the interest worldly for many years. Here, it is pointed out that this approach is different from the previous results in the following detailed items:
(b) With respect to the lumped parameter ladder network model derived from interconnection lines in digital circuits, the tightest estimates of bounds for global switching time in the related literature are obtained.
(c) In the light of two classes of assumptions, decay estimates are originally established for solutions of two families of Razumikhin-type functional differential equations (FDE), which play an important role in many related contributions. From the point of applications of Razumikhin-type theorems, this work is also an extension of the ones reported so far in the related literature.
(d) Originally, the quantitative description for the stability of solutions is presented for a family of scalar time varying delay differential inequalities, which are generally encountered and become key problems in the course of the stability analysis for retarded systems in engineering.
(e) Initial studies in delay-dependent quantitative stability criteria for two
(a)从信息的观点，给出控制、时延相关稳定判据和时延不相关稳定判据的概念描述。提出神经网络的函数逼近定义。从数学描述上看，神经网络应用应以所要研究的对象特性为出发点。所以，作者认为神经网络的定义也应与相应的目标函数密切相关。对于相同的非线性对象，神经网络的不同会影响应用的效果和神经网络本身的复杂性。
实际中，存在于通讯设备和实际系统本身的时延扰动无处不在，并且通常被认为是一个重要的不稳定因素。因此，研究时延系统的特性，有着重要的意义。而且，在研究系统的稳定性过程中，专家们不但想得到关于稳定性的定性描述，更希望得到关于实际系统解的过渡过程的定量信息。所以，许多年来，定量稳定性研究一直得到广泛关注。本文在这方面的研究成果与其他学者贡献的区别在于以下几点：
(b)关于数字电路中连接线的块状参数梯形网络模型，给出迄今为止最紧的全局开关延迟时间的估计界限。
(c)基于两类假设，开创性地研究两类Razumikhin型泛函微分方程(FDE)解的衰变估计。所研究的这些FDE在许多研究成果中发挥着重要作用。从Razumikhin定理的应用角度出发，相关文献中的众多结果可以得到相应的拓广。
(d)对于在实际时延系统的稳定性分析的过程中经常遇到，并且成为关键问题的一类标量时变时延微分不等式，创造性地构造出其解的稳定性的定量描述形式。
(e)首次提出带有输入时延扰动的LQ调节器和静态输出反馈控制器的时延相关定量稳定性判据。
(f)创造性地导出具有时变时延扰动的神经动态系统的全局时延不相关定量稳定性判据。扩展这方面关于时延不相关稳定性研究的已知结果，并且给出神经网络状态轨迹的衰变估计。
(g)研究检验带有扰动的滞后型泛函微分方程(RFDE)正不变集的条件，并且首次引入带有非线性输入时延扰动的线性系统状态的正不变集概念，给出这类系统状态的非对称正不变集检验的充分条件。
本文的总体结构安排如下：
(a)在第一章中，对一个富有挑战性的课题一时延系统的主要进展和发展趋势进行系统地综述，引入控制、神经网络和稳定性概念。
(b)正象以前的研究成果所指出的那样，电子电路中连接线上时延的研究，具有基础的重要性。在本文第二章，以电路分析中通常采用的带有电容负载的n
General conceptions in engineering can be viewed as the operation of the information. Plan and action are two important conceptions in the procedure to operate information. The first is to investigate the information while the other is to employ the obtained information to achieve the motivation efficiently. The action with respect to information consists of the motivation and the approximation. So, I think the first reasonable contribution in this work is stated as follows.
(a) The basic conceptions, such as control, delay-dependent stability criteria, and delay-independent stability criteria, are defined from the point of information. In the light of the function approximation approach, the definition of general neural networks is presented. From the description of mathematics, applications of neural networks should be based on the investigations of the practical systems. Hence, the author think that the definition of neural networks is related to the functions to be modeled. The performance of systems and the complexities of neural networks are adjustable as different neural networks are applied to the same plant.
Time delay perturbations, which exist in communication equipment and plants, are ubiquitous and generally regarded as sources of instability in the practical engineering. So, it is of important to study the performance of retarded engineering systems. Moreover, in the procedure of stability analysis, experts are not only interested in the stability properties, but also in quantitative transient characteristics of solutions of systems. Therefore, the investigation on the quantitative stability has reasonably attracted the interest worldly for many years. Here, it is pointed out that this approach is different from the previous results in the following detailed items:
(b) With respect to the lumped parameter ladder network model derived from interconnection lines in digital circuits, the tightest estimates of bounds for global switching time in the related literature are obtained.
(c) In the light of two classes of assumptions, decay estimates are originally established for solutions of two families of Razumikhin-type functional differential equations (FDE), which play an important role in many related contributions. From the point of applications of Razumikhin-type theorems, this work is also an extension of the ones reported so far in the related literature.
(d) Originally, the quantitative description for the stability of solutions is presented for a family of scalar time varying delay differential inequalities, which are generally encountered and become key problems in the course of the stability analysis for retarded systems in engineering.
(e) Initial studies in delay-dependent quantitative stability criteria for two
引文
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