<p> Motivated by the increasing need to monitor safety-critical systems subject to uncer-<br> tainties, a novel set-membership approach is proposed to estimate the state of a dynamical<br> system with unknown-but-bounded exogenous inputs. By fully utilizing the system struc-<br> tural information, the proposed algorithm can address both computational efficiency and<br> estimation accuracy without requiring restrictive conditions on the system. Particularly,<br> the system is first decomposed into the strongly observable subsystem and the weakly un-<br> observable subsystem. To make full use of the subsystem’s properties, a set-membership<br> observer based on the unknown input observer and an ellipsoidal set-membership observer<br> are designed for the two subsystems, respectively. Then, the resulting set estimates from<br> each subsystem are fused and transformed to obtain the set estimate for the original system,<br> which is guaranteed to bound the actual system state. The conditions for the boundedness<br> of the proposed set estimate are discussed, and the proposed set-membership observer is also<br> tested numerically using illustrative examples.</p>