Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach
Stability Analysis of Networked Control Systems Using a Switched Linear Systems Approach
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DOI：
10.1007/978-3-642-00602-9_11
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发表时间：
2009-04
影响因子：
6.8
通讯作者：
M. Donkers;L. Hetel;W. Heemels;N. Wouw;M. Steinbuch;R. Majumdar;P. Tabuada
中科院分区：
文献类型：
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作者：
M. Donkers;L. Hetel;W. Heemels;N. Wouw;M. Steinbuch;R. Majumdar;P. Tabuada
在本文中，我们研究的网络控制系统（NCSs）的稳定性，是时变的传输间隔，时变的传输延迟，和通信约束。通信约束强加于每个传输，只有一个节点可以访问网络并发送其信息。节点发送其信息的顺序由网络协议（诸如，循环（RR）和尝试一次丢弃（TOD）协议）编排。在本文中，我们将上述协议推广到新的所谓的“周期性”和“二次”协议类。针对线性对象和控制器，提出了一种基于离散切换线性不确定系统的网络控制系统建模框架。该框架允许控制器在离散时间以及在连续时间。为了分析这种系统的稳定性的范围内可能的传输间隔和延迟，与可能的非零下界，我们提出了一个新的程序，以获得凸过逼近的形式的多面体系统与范数有界的附加不确定性。我们表明，这种近似可以在适当的意义上任意紧。基于这种过度逼近，我们得到稳定性的结果，在线性矩阵不等式（LMI）。我们说明了我们的稳定性分析的基准示例的间歇式反应器，并显示这是如何导致不同的协议之间的权衡，允许的范围内的传输间隔和延迟。此外，我们表明，利用系统和控制器的线性导致显着减少保守性与文献中现有的方法。
In this paper, we study the stability of networked control systems (NCSs) that are subject to time-varying transmission intervals, time-varying transmission delays, and communication constraints. Communication constraints impose that, per transmission, only one node can access the network and send its information. The order in which nodes send their information is orchestrated by a network protocol, such as, the Round-Robin (RR) and the Try-Once-Discard (TOD) protocol. In this paper, we generalize the mentioned protocols to novel classes of so-called “periodic” and “quadratic” protocols. By focusing on linear plants and controllers, we present a modeling framework for NCSs based on discrete-time switched linear uncertain systems. This framework allows the controller to be given in discrete time as well as in continuous time. To analyze stability of such systems for a range of possible transmission intervals and delays, with a possible nonzero lower bound, we propose a new procedure to obtain a convex overapproximation in the form of a polytopic system with norm-bounded additive uncertainty. We show that this approximation can be made arbitrarily tight in an appropriate sense. Based on this overapproximation, we derive stability results in terms of linear matrix inequalities (LMIs). We illustrate our stability analysis on the benchmark example of a batch reactor and show how this leads to tradeoffs between different protocols, allowable ranges of transmission intervals and delays. In addition, we show that the exploitation of the linearity of the system and controller leads to a significant reduction in conservatism with respect to existing approaches in the literature.