On the Lyapunov equation in Banach spaces and applications to control problems (Q1607829)

The authors consider the equivalence between the solvability of the Lyapunov equation and exponential stability of a linear system in a Banach space. Moreover they establish the relationship between stabilizability and exact null-controllability of linear control systems and then give some applications to the exponential stabilizability of a class of nonlinear control systems in Banach space by using the Lyapunov theorem. The results of this paper can be considered as a further development of results obtained earlier.