Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems
Periodically time-varying memory state-feedback controller synthesis for discrete-time linear systems
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DOI：
10.1016/j.automatica.2010.10.004
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发表时间：
2011
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影响因子：
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通讯作者：
Y. Ebihara;D. Peaucelle;D. Arzelier
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文献类型：
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作者：
Y. Ebihara;D. Peaucelle;D. Arzelier
本文针对具有多面体型不确定性的离散线性周期/时不变系统，提出了一种基于线性矩阵不等式(LMI)的鲁棒状态反馈控制器综合方法。与仅限于无记忆静态控制器综合的现有方法形成鲜明对比的是，我们探索了动态控制器综合，并揭示了一种特殊的周期性时变记忆状态反馈控制器(PTVMSFC)结构，该结构允许基于LMI的综合。在鲁棒控制器综合的背景下，我们严格地证明了所提出的设计方法包含了著名的基于扩展LMI的静态控制器综合方法作为特例。通过数值实验，我们证明了所提出的设计方法在周期和时不变设置下都能获得较小保守性的结果。最后，我们得到了一个可行的测试来验证所设计的鲁棒PTVMSFC是“精确的”，即它获得了最佳的可实现的鲁棒性能。这种精确度验证测试在实践中效果良好，我们将通过一个数值例子说明，即使对于这样一个标准的无记忆静态反馈失效的问题，通过设计PTVMSFC确实可以获得精确的鲁棒控制。
In this paper, we deal with discrete-time linear periodic/time-invariant systems with polytopic-type uncertainties and propose a new linear matrix inequality (LMI)-based method for robust state-feedback controller synthesis. In stark contrast with existing approaches that are confined to memoryless static controller synthesis, we explore dynamical controller synthesis and reveal a particular periodically time-varying memory state-feedback controller (PTVMSFC) structure that allows LMI-based synthesis. In the context of robust controller synthesis, we prove rigorously that the proposed design method encompasses the well-known extended-LMI-based static controller synthesis methods as particular cases. Through numerical experiments, we demonstrate that the suggested design method is indeed effective in achieving less conservative results, under both periodic and time-invariant settings. We finally derive a viable test to verify that the designed robust PTVMSFC is “exact” in the sense that it attains the best achievable robust performance. This exactness verification test works fine in practice, and we will show via a numerical example that exact robust control is indeed attained by designing PTVMSFCs, even for such a problem where the standard memoryless static state-feedback fails.