SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1275-1292, January 2021.
We study infinite-time admissibility and infinite-time exact observability of Volterra systems in Hilbert spaces using a Hardy space approach, with an emphasis on the former. The problem is reduced to boundedness and lower boundedness of the associated weighted composition operators on the Hardy space on the right half plane. Sufficient conditions are established under which infinite-time admissibility and infinite-time exact observability of a Volterra system follows from that of the corresponding Cauchy system without convolution term. For infinite-time admissibility, the special case of exponentially decaying kernels is considered and two illustrative examples are given, both infinite-dimensional and infinite-dimensional. In the infinite-dimensional example, the obtained theoretical results are verified by numerical simulations.

中文翻译：

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Volterra系统的无限时间可容许性和精确可观测性

SIAM控制与优化杂志，第59卷，第2期，第1275-1292页，2021年1月。
我们使用Hardy空间方法研究了希尔伯特空间中Volterra系统的无限时间可容许性和无限时间精确可观性，重点是前者。问题减少到右半平面上Hardy空间上相关加权合成算子的有界和较低界。建立了充分的条件，在这些条件下，Volterra系统的无限时间可容许性和无限时间的精确可观测性要遵循相应的不带卷积项的柯西系统的可观测性和无限时间的可观测性。对于无限时间可容许性，考虑了指数衰减核的特殊情况，并给出了两个说明性示例，即无限维和无限维。在无穷大实例中，通过数值模拟验证了所获得的理论结果。