Closed-loop asymptotic stability and robustness conditions for large space systems with reduced-order controllers

Velocity-sensor outputs can be fed back for augmentation of damping to large space structures and displacement-sensor outputs can for augmentation of stiffness. The design of feedback controllers for such distributed-parameter systems in practice must be based on only a relatively small number of modeled modes, however. Usually, the existence of spillover and the interaction with unmodeled modes are ignored: even stability of full-order closed-loop (FOCL) system with reduced-order (RO) feedback controllers is not ensured, let alone the additional damping and stiffness desired. This paper presents various useful conditions for ensuring FOCL asymptotic stability. Such conditions and the insights thereby derived are useful as a guide to FOCL asymptotic stability ensuring designs of RO feedback controllers. Large space systems considered are not limited to the class of large space structures; possible presence of rigid or unstable modes are not excluded. For the common class of large space structures having only stable (elastic or rigid) modes, specially useful simpler conditions for ensuring FOCL asymptotic stability are also given; so are conditions for robustness of FOCL asymptotic stability to parameter errors.