  This paper studies the uncertainty set estimation of system parameters of
linear dynamical systems with bounded disturbances, which is motivated by
robust (adaptive) constrained control. Departing from the confidence bounds of
least square estimation from the machine-learning literature, this paper
focuses on a method commonly used in (robust constrained) control literature:
set membership estimation (SME). SME tends to enjoy better empirical
performance than LSE's confidence bounds when the system disturbances are
bounded. However, the theoretical guarantees of SME are not fully addressed
even for i.i.d. bounded disturbances. In the literature, SME's convergence has
been proved for general convex supports of the disturbances, but SME's
convergence rate assumes a special type of disturbance support: $l_\infty$
ball. The main contribution of this paper is relaxing the assumption on the
disturbance support and establishing the convergence rates of SME for general
convex supports, which closes the gap on the applicability of the convergence
and convergence rates results. Numerical experiments on SME and LSE's
confidence bounds are also provided for different disturbance supports.
