Application of set-membership identification to lightly damped systems

In this paper, we consider the problem of determining bounds on the uncertainty of lightly damped systems. We assume we have frequency domain input-output data. The system is parameterized in a way which is appropriate for modern robust control techniques. Bounds on the parameters of this model are then determined using set-membership identification. The a priori information necessary is a rough estimate of the natural frequency for each mode, an upper bound on the damping ratio for each mode, an upper bound on the error in each mode at points away from its natural frequency, and an upper bound on the magnitude of the noise as a function of frequency.