General decay of a flexible satellite system under unknown distributed disturbances

This work is concerned with a flexible satellite system. The problem subject to some undesirable vibrations and a distributed disturbances. The system can be modelled as a lumped mass and two flexible cantilever Euler-Bernoulli beams with memory-type governed by a set of non-homogeneous partial differential equations taking into account therefore the dynamic boundary conditions. We prove the existence and uniqueness of solutions of the system as well as some new general decay results which generalise and improve many earlier ones in the literature. Finally, simulation results are demonstrated for control performance verification.