离散时间线性系统的鲁棒镇定需要非线性动态反馈
Robust stabilization of discrete-time linear systems requires nonlinear dynamic feedback
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中文总结 AI 辅助
本文针对离散时间线性输入状态系统的鲁棒镇定问题，证明了部分可镇定系统的紧集无法用非线性静态或线性动态反馈实现鲁棒镇定，需非线性动态反馈，还扩展了指数镇定研究并提出多面体系统的反馈设计算法。
中文摘要 AI 辅助
本文研究离散时间线性输入状态系统的鲁棒镇定问题。我们证明，对于任意一组可镇定系统的紧集，存在一个动态状态反馈控制器，能全局渐近镇定该集合中的所有系统。此外，我们表明，对于部分可镇定系统的紧集，不存在非线性静态或线性动态状态反馈律可完成该任务，这证明了一般情况下鲁棒镇定需要同时是非线性且动态的反馈律。我们将研究扩展到具有给定衰减率的鲁棒指数镇定。最后，针对多面体系统集合，我们提出了一种鲁棒反馈律的设计算法。
英文摘要
This paper studies the problem of robust stabilization of linear input-state systems in discrete time. We prove that for any compact set of stabilizable systems, there exists a dynamic state-feedback controller that globally asymptotically stabilizes all systems in the set. In addition, we show that for some compact sets of stabilizable systems, no nonlinear static or linear dynamic state-feedback law can achieve this task. This proves that, in general, robust stabilization requires a feedback law that is both nonlinear and dynamic. We extend our study to robust exponential stabilization with a given rate of decay. Finally, for polytopic sets of systems, we introduce an algorithm for the design of robust feedback laws.
