FEEDBACK LAW TO STABILIZE LINEAR INFINITE-DIMENSIONAL SYSTEMS

We design a new feedback law to stabilize the linear infinite dimensional control system, where the state operator generates a C0-group, and the control operator is unbounded. Our feedback law is based on the integration of a mutated Gramian operator-valued function. In the structure of the aforementioned mutated Gramian operator, we utilize the weak observability inequality in [21, 13] and borrow some idea used to construct generalized Gramian operators in [11, 23, 24]. Unlike most related works where the exact controllability is required, we only assume the above-mentioned weak observability inequality, which is equivalent to the stabilizability of the system.