Bounded input delay frequently arises in discrete‐time linear systems. The standard predictor feedback design requires the exact knowledge of the delay. Such a requirement on the availability of the delay knowledge poses challenges in the design of robust control laws when only the knowledge of an upper bound of the delay is known. We propose such a design in this article. Based on the delay‐independent truncated predictor state feedback design, an observer‐based output feedback law is constructed that does not contain any explicit information of the delay. For a general, possibly exponentially unstable, discrete‐time linear system, the proposed output feedback law stabilizes the system as long as the delay does not exceed a certain amount. For the special case of systems with all the open‐loop poles on or inside the unit circle, a low gain feedback design is presented. This low gain design allows us to establish that, when all the open‐loop poles of a system are at z = 1 or inside the unit circle, stabilization can be achieved for an arbitrarily large bounded delay as long as the value of the low gain parameter is chosen small enough.

中文翻译：

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具有未知输入延迟的离散线性系统的与时滞无关的输出反馈律

在离散时间线性系统中，有界输入延迟经常出现。标准的预测器反馈设计需要对延迟有确切的了解。当仅知道延迟上限的知识时，对延迟知识的可用性的这种要求在鲁棒控制定律的设计中提出了挑战。我们在本文中提出了这样的设计。基于不依赖于延迟的截断的预测器状态反馈设计，构建了基于观察者的输出反馈律，该律不包含任何明显的延迟信息。对于一般的，可能是指数不稳定的离散时间线性系统，只要延迟不超过一定数量，建议的输出反馈定律会使系统稳定。对于在单位圆内或单位圆内具有所有开环极点的系统的特殊情况，提出了一种低增益反馈设计。这种低增益设计使我们能够确定，当系统的所有开环极点都在z  = 1或在单位圆内，只要将低增益参数的值选择得足够小，就可以对任意大的有界延迟实现稳定。