SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 466-486, February 2024.
Abstract. We study Jeffreys-type overdamped second order linear systems with observed outputs in the setting of Hilbert spaces. The state equation comes from an overdamped second order linear partial differential equation which is wave-like but was proposed to describe heat conduction. It results from adopting the Jeffreys law of constitutive relation for heat flux, rather than the usual Fourier law. Sufficient conditions for infinite-time admissibility of the system observation operator and system observability are obtained. In the general case, we obtain the infinite-time admissibility from that of the first order Cauchy system, which is done by employing the Hardy space approach. In the special case when the operator in the state equation is negative definite, we derive the infinite-time admissibility and system observability using a semigroup approach. Illustrative examples are given.

中文翻译：

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Jeffreys型过阻尼二阶线性系统的容许性和可观性

SIAM 控制与优化杂志，第 62 卷，第 1 期，第 466-486 页，2024 年 2 月。
摘要。我们研究杰弗里斯型过阻尼二阶线性系统，并在希尔伯特空间的设置中观察到输出。状态方程来自过阻尼二阶线性偏微分方程，该方程是波状的，但被提出来描述热传导。它是由于采用热通量本构关系的杰弗里斯定律而不是通常的傅立叶定律而产生的。得到了系统观测算子无限时间可容许性和系统可观测性的充分条件。在一般情况下，我们通过使用 Hardy 空间方法从一阶柯西系统获得无限时间的可容许性。在状态方程中的算子为负定的特殊情况下，我们使用半群方法推导了无限时间的容许性和系统的可观性。给出了说明性例子。