论文标题
Banach空间中线性和双线性无界系统的反馈稳定
Feedback stabilization of linear and bilinear unbounded systems in Banach space
论文作者
论文摘要
我们考虑形式的线性控制系统$ \ dot {y}（t）= ay（t）-μbc y（t）$，其中$μ$是一个积极的实际参数，$ a $是国家运营商，并在Banach Space $ x $ $ x $ $ x $ $ x $ $ x $ c的$ c_0- $ c_0- $ c_0- $ semigroup semigroup semigroup contractions $ s（t）$ s（$从某种意义上说，它们没有边界。我们旨在在足够的条件下显示上述系统的指数稳定性，这些条件以可接受性和可观察性特性表示。也考虑了使用双线性控制的均匀指数稳定。还提供了运输和热方程式的应用。
We consider linear control systems of the form $\dot{y}(t)=Ay(t)-μB C y(t)$ where $μ$ is a positive real parameter, $A$ is the state operator and generates a linear $C_0-$semigroup of contractions $S(t) $ on a Banach space $X$, $B$ and $C$ are respectively the operators of control and observability, which are defined in appropriate spaces in which they are unbounded in some sense. We aim to show the exponential stability of the above system under sufficient conditions which are expressed in term of admissibility and observability properties. The uniform exponential stabilization using bilinear control is considered as well. Applications to transport and heat equations are also provided.
