  This paper studies uncertainty set estimation for unknown linear systems.
Uncertainty sets are crucial for the quality of robust control since they
directly influence the conservativeness of the control design. Departing from
the confidence region analysis of least squares estimation, this paper focuses
on set membership estimation (SME). Though good numerical performances have
attracted applications of SME in the control literature, the non-asymptotic
convergence rate of SME for linear systems remains an open question. This paper
provides the first convergence rate bounds for SME and discusses variations of
SME under relaxed assumptions. We also provide numerical results demonstrating
SME's practical promise.
