论文标题
完全稳定性的特征
Characterizations of complete stabilizability
论文作者
论文摘要
We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system $[A,B]$, i.e., $y'(t)=Ay(t)+Bu(t)$, $t\geq 0$, where $A$ generates a $C_0$-semigroup on a Hilbert space $X$ and $B$ is a linear and bounded operator from another Hilbert space $U$ to $ x $。然后，我们将上述特征扩展到两个方向：首先，控制操作员$ b $是无限的；其次，控制系统是时间周期性的。从光谱预测的角度来看，我们还提供了一些足够的条件，以确保弱的观察力不平等。作为应用程序，我们提供了几个示例，这些示例不是无效的，但可以通过弱的可观察性不平等来验证，以完全稳定。
We present several characterizations, via some weak observability inequalities, on the complete stabilizability for a control system $[A,B]$, i.e., $y'(t)=Ay(t)+Bu(t)$, $t\geq 0$, where $A$ generates a $C_0$-semigroup on a Hilbert space $X$ and $B$ is a linear and bounded operator from another Hilbert space $U$ to $X$. We then extend the aforementioned characterizations in two directions: first, the control operator $B$ is unbounded; second, the control system is time-periodic. We also give some sufficient conditions, from the perspective of the spectral projections, to ensure the weak observability inequalities. As applications, we provide several examples, which are not null controllable, but can be verified, via the weak observability inequalities, to be completely stabilizable.
