摘 要

网络控制系统是一种集计算机、网络、通信与控制等技术于一体的高级控制系统，是通过通信网络和控制系统实现闭环控制的反馈控制系统。随着科学技术的不断发展和进步，网络控制系统的应用也越来越广泛，尤其是在许多控制领域中，比如远程教育、远程医疗以及家庭办公等领域，网络控制的优势在逐渐的显现出来。在实际应用中，它不但可靠性高、灵活性好，而且能实现资源共享和远程控制，这和传统的控制模式相比，具有很强的优越性和现实意义。因此，对网络控制系统的研究是当今社会各界研究领域的重中之重。

在网络控制系统中，被控对象、传感器、控制器以及驱动器由一个有限带宽的数字通信网络连接，通过有线网或无线网来传递控制信息。而网络的带宽总是有限的，因此数据包在传输的过程中会不可避免的出现排队等待的现象，而这一现象最终会导致数据传输的延迟，即网络时滞。另外，在网络环境下，系统还有可能出现数据丢包、网络调度等问题。因此，基于传统控制系统的研究方法不能用于网络控制系统中，我们必须针对网络控制系统的特点给出控制的新思想、新方法，得出最适合网络控制系统的研究方法。

本文对不确定时延的网络控制系统的稳定性进行了研究，建立了适当的系统模型，并利用李雅普诺夫泛函法和线性矩阵不等式给出了系统的稳定性判据和网络控制系统进入稳定的充分条件，利用鲁棒控制理论对不确定时延网络控制系统的稳定性进行了分析研究，并进行了性能分析。然后利用LMI工具箱给出结果，并用SIMULINK仿真验证结论的正确性，并给出系统的状态响应图。

最后，本文对研究的所有内容进行了总结，并指出了下一步要研究的内容，对网络控制系统的稳定性分析进行了展望。

关键词：网络控制系统、李雅普诺夫泛函法、线性矩阵不等式、稳定性分析

Stability Analysis of Networked Control Systems

ABSTRACT

The networked control system is a kind of advanced control system which is combined with computer technology, communication systems, network, control and so on. It’s a feedback control system which can realize closed loop control through communication network and control system. With the continuous development and advancement of science technology, the networked control system is applied more and more widely, especially in some control field, such as the remote education, the telemedicine, the home office and so on, where its advantages are gradually revealed. In practical application, it not only has high reliability, good flexibility but also can realize resources sharing and remote control. Compared with traditional control mode, it has strong superiority and practical significance. Therefore, the study of networked control system is the top priority in the research field of the society.

In networked control system, the controlled object, sensor, controller and driver in this system are connected with the digital communication network of limited bandwidth. Meanwhile, it can deliver controlled message through wired or wireless networks. But the bandwidth of the network is always limited; the packet will inevitably appear the phenomenon of waiting in line in the process of transmission, which will result in delay of data transmission..In addition, problems may occur in the network environment, such as the data packet loss and network scheduling and so on. Therefore, based on the traditional research methods of the control system can’t apply to networked control system. We must get the new ideas and new methods in control which is most suitable for the networked control system, according to the characteristics of the networked control system.

This article discusses the stability of uncertain time delay and builds suitable system mode. Besides, this article gives the stability criterion of the system and sufficient conditions for the robust stability of the networked control system into with Lyapunov functional method and linear matrix inequality(LMI). In addition, it analyzes the stability of uncertain time delay networked control system through the robust control theory. Meanwhile, it studys design problems of robust H infinite output feedback controller of any order and designs controller. As long as the corresponding matrix inequalities exist definite solutions, we can design H output feedback controller of any order. Then this article gets the results with LMI toolbox and verifies the correctness of the conclusion with SIMULINK and gives the state response figure of this system.

In the end, this article summarizes all study content and points out the next research content and then looks forward to stability analysis of the networked control system.

Keywords: the networked control system, the Lyapunov functional method, linear matrix inequality (LMI), the stability analysis

目 录

1 绪论 1

1.1 引言 1

1．2 研究的目的和意义 1

1.3 网络控制系统的结构 2

1.4 网络控制系统的基本问题 3

1.4.1 网络时滞 3

1.4.2 数据丢包 4

1.4.3 网络调度 4

1.4.4 单包传输和多包传输 5

1.4.5 采样和延迟 5

1.4.6 节点驱动方式 6

1.5 国内外研究概况 6

1.6 本文的主要内容 7

2 基本数学知识 9

2.1 Lyapunov泛函法的基本概念 9

2.1.1 Lyapunov方程 9

2.1.2 Lyapunov稳定性的概念 9

2.2 线性矩阵不等式的基本概念 10

2.2.1 LMI应用的基本问题 10

2.2.2 LMI工具箱的基本介绍 11

3 具有不确定时延的网络控制系统的稳定性分析 12

3.1 系统建模 12

3.2 稳定性分析 15

3.3 算例仿真 25

3.4 本章小结 28

4 总结与展望 29

4．1 结论 29

4.2 今后研究方向 29

致 谢 31

参考文献 32

符 号 集

从传感器到控制器的传输延迟

从控制器到执行器的传输延迟