Minimum Data Rate for Mean Square Stabilizability of Linear Systems With Markovian Packet Losses
Minimum Data Rate for Mean Square Stabilizability of Linear Systems With Markovian Packet Losses
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DOI：
10.1109/tac.2010.2068590
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发表时间：
2011-04
期刊：
影响因子：
--
通讯作者：
Keyou You;Lihua Xie
中科院分区：
文献类型：
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作者：
Keyou You;Lihua Xie
本文研究了有损数字信道上线性系统均方可镇定性的最小数据率。信道的数据包丢失过程被建模为一个时间齐次马尔可夫过程。为了克服由数据包丢失过程的时间相关性以及由于数据包丢失导致的数据率随机时变所带来的困难，开发了一种随机采样系统方法来研究均方可镇定性的最小数据率。结果表明，标量系统的最小数据率可以根据不稳定模式的幅度和马尔可夫链的转移概率明确给出。精确量化了抵消马尔可夫数据包丢失对可镇定性影响所需的额外比特数。我们的结果包含了线性标量系统可镇定性的现有数据率和数据包丢失率结果作为特殊情况，并通过联合考虑每样本比特数和有效采样提供了一种更好地利用带宽的方法。分别给出了向量系统均方可镇定性最小数据率问题的充分必要条件，并在一些特殊情况下证明是最优的。
This paper investigates the minimum data rate for mean square stabilizability of linear systems over a lossy digital channel. The packet dropout process of the channel is modeled as a time-homogeneous Markov process. To overcome the difficulties induced by the temporal correlations of the packet dropout process and stochastically time-varying data rate due to packet dropouts, a randomly sampled system approach is developed to study the minimum data rate for mean square stabilizability. It is shown that the minimum data rate for scalar systems can be explicitly given in terms of the magnitude of the unstable mode and the transition probabilities of the Markov chain. The number of additional bits required to counter the effect of Markovian packet losses on stabilizability is exactly quantified. Our result contains existing results on data rate and packet dropout rate for stabilizability of linear scalar systems as special cases and provides a means for better bandwidth utilization by jointly considering bits per sample and an effective sampling. Necessary and sufficient conditions on the minimum data rate problem for mean square stabilizability of vector systems are provided respectively and shown to be optimal under some special cases.