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An Equalization Approach to Feedback Stabilization Over Fading Channels

机译：衰落信道上反馈稳定的均衡方法

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摘要

This paper proposes an equalization approach to mean-square (MS) feedback stabilization for multi-input/multi-output (MIMO) discrete-time systems over fading channels. An orthogonal encode/decode matrix pair is placed at the two ends of the fading channel, thereby equalizing the complementary sensitivity in the MS sense. By adopting the notion of the MS stability in an input-output setting, and using the signal-to-noise ratio (SNR) and encode/decode matrix as additional design parameters, we are able to convert the networked stabilization over fading channels into an equivalent constrained optimal control, and derive the MS stabilizability conditions over linear time-invariant controllers. Our results recover the existing MS stabilizability condition under the state feedback. For output feedback control, we provide a characterization of the minimum network resource for the SNR required to stabilize the networked control system over the fading channel, and develop the synthesis algorithms for design of the orthogonal coding matrix and output feedback controller in different scenarios. Our results show that the MS stabilization problem as formulated in this paper admits the closed-form solution for MIMO plants with unstable block zeros, and is mathematically tractable for more general MIMO plants. Two numerical examples are worked out to illustrate our results.
机译：本文提出了一种用于衰落信道上的多输入/多输出（MIMO）离散时间系统的均方（MS）反馈稳定化均衡方法。正交编码/解码矩阵对放置在衰落信道的两端，从而使MS方向上的互补灵敏度相等。通过在输入输出设置中采用MS稳定性的概念，并将信噪比（SNR）和编码/解码矩阵用作附加设计参数，我们能够将衰落信道上的网络稳定度转换为等效约束最优控制，并推导线性时不变控制器的MS稳定性条件。我们的结果恢复了状态反馈下现有的MS稳定性条件。对于输出反馈控制，我们提供了在衰落信道上稳定网络控制系统所需的SNR所需的最小网络资源的特性，并开发了用于在不同情况下设计正交编码矩阵和输出反馈控制器的综合算法。我们的结果表明，本文提出的MS稳定问题适用于具有不稳定块零的MIMO设备的闭式解决方案，并且对于更一般的MIMO设备在数学上很容易解决。通过两个数值例子说明了我们的结果。

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