Abstract In the paper we consider the problem of exact observability of a general class of distributed parameter systems in Hilbert spaces. We show that under some conditions on asymptotic behavior of the spectrum of the differential operator the system is not exact observable in default topologies, and find a stronger topology for state observation for which the system becomes exactly observable. We illustrate this result with a vibrating clamped-free Timoshenko beam model.

中文翻译：

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希尔伯特空间动力系统的精确可观测条件与分差的 Riesz 基有关

摘要 本文考虑了一类广义分布参数系统在希尔伯特空间中的精确可观测性问题。我们表明，在微分算子谱的渐近行为的某些条件下，系统在默认拓扑中不是精确可观测的，并找到了一种更强的拓扑结构来进行状态观测，从而使系统变得完全可观测。我们用一个振动夹紧的 Timoshenko 梁模型来说明这个结果。