Two simple criterion to obtain exact controllability and stabilization of a linear family of dispersive PDE's on a periodic domain (Q2089104)

In this paper, the authors establish a criterion to determine whether a family of linearized dispersive equations on a one dimensional periodic domain is exactly controllable and exponentially stabilizable with any given decay rate in suitable Sobolev space. The main method they employ is the moment method. As applications of that criterion, the study the controllability and stabilization problems for the linearized Smith equation, the linearized dispersion generalized Benjamin-Ono equation, the linearized fourth-order Schrödinger equation, and the higher-order Schrödinger equations on a one dimensional periodic domain.