Optimality of simple dynamic displacement feedback for large space structures

In this paper, an optimal output feedback is considered for a large space structure (LSS) described by a second order differential equation. It has been known that the direct velocity and displacement feedback (DVDFB) or the simple dynamic displacement feedback (SDDFB) can stabilize the LSS with collocated sensors and actuators robustly against any parameter uncertainty in mass, damping, and stiffness. Furthermore, it has also been shown that if the gains of the DVDFB are selected appropriately, the DVDFB is optimal with respect to a quadratic performance index. The objective of this paper is to extend this idea to the case of the SDDFB. It is shown that, if the gains of the SDDFB are selected suitably, the SDDFB is also optimal with respect to a quadratic performance index.