  In this paper, we address the problem of robust stability for uncertain
sampled-data systems controlled by a discrete-time disturbance observer
(DT-DOB). Unlike most of previous works that rely on the small-gain theorem,
our approach is to investigate the location of the roots of the characteristic
polynomial when the sampling is performed sufficiently fast. This approach
provides a generalized framework for the stability analysis in the sense that
(i) many popular discretization methods are taken into account; (ii) under fast
sampling, the obtained robust stability condition is necessary and sufficient
except in a degenerative case; and (iii) systems of arbitrary order and of
large uncertainty can be dealt with. The relation between sampling
zeros---discrete-time zeros that newly appear due to the sampling---and robust
stability is highlighted, and it is explicitly revealed that the sampling zeros
can hamper stability of the overall system when the Q-filter and/or the nominal
model are carelessly selected in discrete time. Finally, a design guideline for
the Q-filter and the nominal model in the discrete-time domain is proposed for
robust stabilization under the sampling against the arbitrarily large (but
bounded) parametric uncertainty of the plant.
