控制算子的可接受性与输入到状态稳定性鲁棒性的研究
Admissibility of control operators for positive semigroups and robustness of input-to-state stability
AI总结：
本文研究了分布式参数系统的well-posedness和稳定性，重点探讨线性正控制系统的特性，推导了正算子控制算子的残差条件，并研究了在无界扰动下的ISS鲁棒性。
摘要：
本文研究了分布式参数系统的well-posedness和稳定性，特别关注线性正控制系统。我们建立了Banach格设置下的well-posedness特征。此外，我们推导了正算子控制算子的残差条件。同时，我们研究了在底层半群生成元的无界扰动下的输入到状态稳定性（ISS）行为。更具体地说，我们建立了在Desch-Schappacher扰动下的ISS鲁棒性的必要和充分条件。我们的理论结果通过具有非局部边界条件的边界值控制传输方程得到验证。
英文摘要：
In this paper, we investigate well-posedness and stability properties of distributed parameter systems, with particular emphasis on linear positive control systems. We establish a characterization of the well-posedness in the Banach lattice setting. Furthermore, we derive a resolvent condition for admissibility of control operators for positive semigroups. In addition, we study the behavior of input-to-state stability (ISS) under unbounded perturbations of the underlying semigroup generator. More precisely, we establish necessary and sufficient conditions for the robustness of ISS under Desch-Schappacher perturbations. Our theoretical results are demonstrated through a boundary value-controlled transport equation with non-local boundary conditions.
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