On continuity of solutions for parabolic control systems and input-to-state stability
On continuity of solutions for parabolic control systems and input-to-state stability
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DOI：
10.1016/j.jde.2018.11.004
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发表时间：
2017-09
影响因子：
2.4
通讯作者：
B. Jacob;Felix L. Schwenninger;H. Zwart
中科院分区：
文献类型：
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作者：
B. Jacob;Felix L. Schwenninger;H. Zwart
研究了线性演化控制系统的温和解对任意有界输入函数连续的极小条件。这个问题在处理边界控制的线性偏微分方程时自然会出现。在这里，我们专注于抛物方程，允许算子理论的方法，如全纯泛函微积分。此外，我们调查更强的条件比连续性导致输入状态稳定性Orlicz空间。这也意味着，输入状态稳定性和积分输入状态稳定性的概念一致，如果另外的不受控方程是耗散的，输入空间是有限维的。
We study minimal conditions under which mild solutions of linear evolutionary control systems are continuous for arbitrary bounded input functions. This question naturally appears when working with boundary controlled, linear partial differential equations. Here, we focus on parabolic equations which allow for operator-theoretic methods such as the holomorphic functional calculus. Moreover, we investigate stronger conditions than continuity leading to input-to-state stability with respect to Orlicz spaces. This also implies that the notions of input-to-state stability and integral-input-to-state stability coincide if additionally the uncontrolled equation is dissipative and the input space is finite-dimensional.