Interdisciplinary Center for Applied Mathematics

Publication Detail

S. Gugercin, A. C. Antoulas, and H. Zhang, "An approach to identification for robust control," IEEE Transactions on Automatic Control, vol. 48, iss. 6, 2003.

AbstractGiven measured data generated by a discrete-time linear system we propose a model consisting of a linear, time-invariant system affected by norm-bounded perturbation. Under mild assumptions, the plants belonging to the resulting uncertain family form a convex set. The approach depends on two key parameters: an a priori given bound of the perturbation, and the input used to generate the data. It turns out that the size of the uncertain family can be reduced by intersecting the model families obtained by making use of different inputs. The model validation problem in this identification scheme is analyzed. For a given energy level, the invalidation problem yields the family of those models which can never be invalidated for any possible input of fixed energy and any possible perturbation; this leads to the intersection of all uncertain families. A consequence of the invalidation problem is that for finite length measurements {\\it not} all models can be invalidated, using fixed-energy inputs.