Discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality (LMI) regions, a class of convex regions of the complex plane that embraces most practically useful stability regions. The focus is on linear systems with static uncertainty on the state matrix. For this class of uncertain systems, the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary LMI regions. The resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities (LMIs) and cover both unstructured and parameter uncertainty. These analysis results are then applied to the synthesis of dynamic output-feedback controllers that robustly assign the closed-loop poles in a prescribed LMI region. With some conservatism, this problem is again tractable via LMI optimization. In addition, robust pole placement can be combined with other control objectives, such as H/sub 2/ or H/sub /spl infin// performance, to capture realistic sets of design specifications. Physically motivated examples demonstrate the effectiveness of this robust pole clustering technique.
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机译：讨论用于线性矩阵不等式（LMI）区域中稳健极点放置的分析和综合技术，该区域是一类包含最实际有用的稳定区域的复杂平面的凸形区域。重点是在状态矩阵上具有静态不确定性的线性系统。对于这类不确定系统，二次稳定性的概念和相关的鲁棒性分析测试可推广到任意LMI区域。鲁棒极点群集的最终测试在数值上都是易于处理的，因为它们涉及求解线性矩阵不等式（LMI），并且涵盖了非结构化和参数不确定性。然后将这些分析结果应用于动态输出反馈控制器的合成，该控制器在指定的LMI区域中稳健地分配闭环极点。出于某种保守，这个问题可以通过LMI优化再次解决。此外，可以将坚固的磁极放置与其他控制目标（例如H / sub 2 /或H / sub / spl infin //性能）结合起来，以获取逼真的设计规范集。出于身体动机的示例证明了这种强大的极点群集技术的有效性。
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