This note presents a new unknown input observer (UIO) with adjustable performances for linear systems. It focuses on state estimation in the presence of zeros with slow dynamics. It is known that if the system has stable invariant zeros and satisfies the decoupling condition then a UIO exists. However, the invariant zeros constrain the pole placement and consequently the state estimation error convergence rate, especially, when the zeros dynamics are slow. In the proposed UIO, the exact decoupling condition is relaxed by the introduction of the asymptotic decoupling notion which allows to act on the invariant zeros and then enhance the convergence rate of the state estimation error. Numerical examples are provided to illustrate the performances of the UIO.

中文翻译：

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关于线性系统的未知输入观察者：渐近未知输入解耦方法

本笔记介绍了一种新的未知输入观测器 (UIO)，其性能可调节，适用于线性系统。它侧重于存在具有缓慢动态的零时的状态估计。已知如果系统具有稳定不变的零点并且满足解耦条件，则存在UIO。然而，不变的零点限制了极点位置，从而限制了状态估计误差的收敛速度，尤其是当零点动态很慢时。在所提出的UIO中，通过引入渐近解耦概念放宽了精确解耦条件，该概念允许作用于不变零点，然后提高状态估计误差的收敛速度。提供了数值示例来说明 UIO 的性能。