A high-order sliding-mode observer is designed for linear time invariant systems with bounded unknown inputs. It provides the global observation of the state under sufficient and necessary conditions of strong observability or strong detectability. The observation is finite-time-convergent and exact in the strongly observable case and asymptotically exact in the strongly detectable case. An unknown input identification algorithm is proposed with finite time convergence for the strongly observable case, and asymptotic convergence for the strongly detectable case. Necessary and sufficient conditions for unknown input identification are given. The unknown input identification algorithm is applied for fault detection. The case of sensor-faults detection is considered without filtration.