Observation of linear systems with unknown inputs via high-order sliding-modes

A high-order sliding-mode observer is designed for linear time invariant systems with single output and unknown bounded single input. It provides for the global observation of the state and the output under sufficient and necessary conditions of strong observability or strong detectability. The observation is finite-time-convergent and exact in the strong observability case. The accuracy of the proposed observation and identification schemes is estimated via the sampling step or magnitude of deterministic noises. The results are extended to the multi-input multi-output case.