Abstract
Transfer matrices of structures with collocated sensors and actuators are symmetric. The symmetry is independent of the entities of mass, damping, or stiffness matrices, and is a nonparametric nature. This paper first shows that for such systems, symmetric controllers are more robust than nonsymmetric ones in stabilization. Then, to utilize the state-space methods in designing symmetric controllers, the class of state equations for symmetric systems is given. The property of state equations of symmetric systems suggests us how to choose the state-feedback gains and observer gains to obtain symmetric observer-based-state-feedback controllers. Finally, symmetric LQG, H2, and H∞ controllers are designed under proper assumptions.
