On the regularity and stability of Pritchard–Salamon systems☆
On the regularity and stability of Pritchard–Salamon systems☆
复制标题
DOI：
10.1016/j.jmaa.2005.05.056
复制
发表时间：
2006-05
影响因子：
1.3
通讯作者：
Xiao-Qing Gu;F. Huang
中科院分区：
文献类型：
--
作者：
Xiao-Qing Gu;F. Huang
设S（S（N），B，−）是（W，V）的Pritchard-Salamon系统，其中W和V是Hilbert空间.设U是Hilbert空间，F∈L（W，U）是容许输出算子，SBF（W，U）是相应的容许扰动C 0-半群.我们证明了C 0-半群SBF（S）分别在W和V上保持C 0-半群S（S）的范数连续性、紧性和解析性.我们还刻画了ΔBF（t）=SBF（t）−S（t）（t>0）的紧性和范数连续性。特别地，我们意外地发现，如果从W到V的嵌入是紧的，则ΔBF（t）在W和V上对t>0是范数连续的。并由此给出了SBF（λ）和S（λ）的谱界与增长界之间的关系，从而得到了一些新的稳定性结果.
Let Σ(S(⋅),B,−) be a Pritchard–Salamon system for (W,V), where W and V are Hilbert spaces. Suppose U is a Hilbert space and F∈L(W,U) is an admissible output operator, SBF(⋅) is the corresponding admissible perturbation C0-semigroup. We show that the C0-semigroup SBF(⋅) persists norm continuity, compactness and analyticity of C0-semigroup S(⋅) on W and V, respectively. We also characterize the compactness and norm continuity of ΔBF(t)=SBF(t)−S(t) for t>0. In particular, we unexpectedly find that ΔBF(t) is norm continuous for t>0 on W and V if the embedding from W into V is compact. Moreover, from this we give some relations between the spectral bounds and growth bounds of SBF(⋅) and S(⋅), so we obtain some new stability results.