Boundary control for a class of pseudo-parabolic differential equations

The boundary stabilization problem for a class of linear and nonlinear pseudo-parabolic differential equations is considered. The proposed control laws are used to achieve global exponential stability for the linear system and semi-global exponential stability for the nonlinear system in the H1H1-sense. An H2H2 bound of the solution for the nonlinear system is also derived. A numerical example is included to illustrate the application of the proposed control laws.