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A high-order sliding-mode observer is designed for linear time invariant systems with bounded unknown inputs, providing for the global observation of the state and the inputs 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
Fridman et al. (Sun,) studied this question.