A new stability result for a flexible satellite system with viscoelastic damping

Abstract

In this paper, we study a viscoelastic flexible satellite under unknown distributed disturbances during attitude maneuvering. The system composed of a rigid central hub that represents the spacecraft with two symmetrical viscoelastic Euler-Bernoulli beams and subject to undesirable vibrations. The problem can be modeled by a set of partial differential equations (PDEs) taking into account therefore the dynamic boundary condition. The well-posedness of the closed-loop system is discussed. By applying a control force at the center body of the spacecraft, we shall suppress these vibrations; namely, we establish stability results of the system under appropriate assumptions imposed on the relaxation function. These new results generalize and improve many results in the literature. Our results are obtained by using the multiplier technique. Numerical simulation results show the effectiveness of the proposed control scheme.