Infinite-Dimensional Input-to-State Stability and Orlicz Spaces
Infinite-Dimensional Input-to-State Stability and Orlicz Spaces
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DOI：
10.1137/16m1099467
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发表时间：
2016-09
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影响因子：
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通讯作者：
B. Jacob;R. Nabiullin;J. Partington;Felix L. Schwenninger
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文献类型：
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作者：
B. Jacob;R. Nabiullin;J. Partington;Felix L. Schwenninger
在这项工作中，研究了具有无界控制算子的线性无限维系统的输入状态稳定性和积分输入状态稳定性之间的关系。尽管特别关注 $L^{\infty}$ 的情况，但输入也考虑了一般函数空间。我们证明积分输入状态稳定性可以用 Orlicz 空间的输入状态稳定性来表征。由于我们考虑线性系统，因此结果也可以根据可接受性来表述。对于具有标量输入的抛物线对角系统，关于 $L^\infty$ 的两个稳定性概念是等效的。
In this work, the relation between input-to-state stability and integral input-to-state stability is studied for linear infinite-dimensional systems with an unbounded control operator. Although a special focus is laid on the case $L^{\infty}$, general function spaces are considered for the inputs. We show that integral input-to-state stability can be characterized in terms of input-to-state stability with respect to Orlicz spaces. Since we consider linear systems, the results can also be formulated in terms of admissibility. For parabolic diagonal systems with scalar inputs, both stability notions with respect to $L^\infty$ are equivalent.