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L2 Stability Analysis of Networked Control Systems Based on Event-triggering
LONG Yuqiang, LING Qiang , ZHENG Wei
School of Information Science and Technology, University of Science and Technology of China, Hefei 230027, China
Abstract:In networked control systems, feedback signals are transmitted through digital communication networks, which makes quantization necessary before the transmission of information. However, quantization error is unavoidable and can degrade the system's performance and even its stability. In order to mitigate performance degradation due to quantization error, we introduce an event-triggering technique into these systems' sampling and control functions. With event-triggering control, micro-processors perform sampling only during certain events, which are often defined as certain error variables that go beyond defined bounds. We propose some conditions to guarantee stability under quantization, which can achieve better (longer) average sampling periods than those by conventional periodic sampling techniques. Moreover, we present some quantization density conditions to guarantee stability during logarithmic quantization. The results of simulations conducted on an example system confirm the effectiveness of the stability conditions, and demonstrate the efficiency of the event-triggering technique.
quantized feedback control     event-triggering     L2 stability
1 引言

2 系统模型

γ可以被看作一个增益，β为一个偏移，G的诱导增益可以看作满足式(1)的所有可能γ的取值中最大的下界值. L2稳定性是事件触发机制中常用到的一种比较实用的稳定，可基于李亚普诺夫函数来判定，判定方法简单实用且诱导增益γ/β可以衡量系统稳态性能.

 图 1 系统结构 Fig. 1 System structure

2.1 事件触发

2.2 对数量化器

1) 如果，则量化器不变，直接量化.

2) 如果|xi|<ai，那么进行缩小，让ai=(σ)aiB，发送缩小指令信号，直到满足1)后量化.

3) 如果x，那么进行放大，让ai=($\frac{1}{\sigma }$)aiB，发送放大指令信号，直到满足1)后量化.

3 带量化的事件触发采样控制系统

4 仿真结果

 图 2 事件触发采样系统状态量 Fig. 2 States of event-triggered sampling system

 图 3 周期采样系统状态量 Fig. 3 States of perodic sampling system

 图 4 对比采样时间 Fig. 4 Comparison of sampling time

 图 5 系统状态量 Fig. 5 States of the system

 图 6 采样间隔 Fig. 6 Sampling intervals

5 总结

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"http://dx.doi.org/10.13976/j.cnki.xk.2016.0171"

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#### 文章信息

LONG Yuqiang, LING Qiang, ZHENG Wei

L2 Stability Analysis of Networked Control Systems Based on Event-triggering

INFORMATION AND CONTROL, 2016, 45(2): 171-176.
http://dx.doi.org/10.13976/j.cnki.xk.2016.0171