论文标题
具有一维输入空间的对角线系统的可接受性
Admissibility of retarded diagonal systems with one-dimensional input space
论文作者
论文摘要
我们调查了对控制操作员$ b $在希尔伯特空间状态延迟的动力系统设置中的无限时间的可接受性对角线和$ u \ in l^2（0，\ infty; \ mathbb {c}）$。我们的方法基于$ l^2 $和hardy space $ h^2（\ mathbb {c} _+）$之间的laplace嵌入。结果是根据$ a $ a $ and $ a_1 $的特征值和代表控制操作员的序列表示的。
We investigate infinite-time admissibility of a control operator $B$ in a Hilbert space state-delayed dynamical system setting of the form $\dot{z}(t)=Az(t)+A_1 z(t-τ)+Bu(t)$, where $A$ generates a diagonal $C_0$-semigroup, $A_1\in\mathcal{L}(X)$ is also diagonal and $u\in L^2(0,\infty;\mathbb{C})$. Our approach is based on the Laplace embedding between $L^2$ and the Hardy space $H^2(\mathbb{C}_+)$. The results are expressed in terms of the eigenvalues of $A$ and $A_1$ and the sequence representing the control operator.
