Feedback law to stabilize linear infinite-dimensional systems

We design a new feedback law to stabilize the linear infinite-dimensional control system, where state operator generates $ C_0 $-group, and is unbounded. Our based on integration of mutated Gramian operator-valued function. In structure aforementioned operator, we utilize weak observability inequality in [21,13] borrow some idea used construct generalized operators [11,23,24]. Unlike most related works exact controllability required, only assume above-mentioned inequality, which equivalent stabilizability system.