Disturbance-decoupling observers for a class of second order distributed parameter systems

This work is concerned with the construction of disturbance-decoupling observers for a class of second order distributed parameter systems. The observer design relies on the knowledge of the operator associated with the spatial distribution of the disturbances. Following the finite dimensional results on disturbance-decoupling observers, a disturbance decoupling observer is proposed for a class of second order distributed parameter systems. Conditions for the solvability of the disturbance-decoupling observer are provided and Lyapunov-based convergence of the position and velocity errors is summarized. Simulations studies for the one-dimensional wave equation with two position measurements are included to illustrate the benefits of the disturbance-decoupling observer.