  Motivated by the increasing need to monitor safety-critical systems subject
to uncertainties, a novel set-membership approach is proposed to estimate the
state of a dynamical system with unknown-but-bounded exogenous inputs. The
proposed method decomposes the system into the strongly observable and weakly
unobservable subsystem in which an unknown input observer and an ellipsoidal
set-membership observer are designed for each subsystem, respectively. The
conditions for the boundedness of the proposed set estimate are discussed, and
the proposed set-membership observer is also tested numerically using
illustrative examples.
