A sliding mode observer for discrete-time linear systems is proposed which can maintain the sliding mode and retains robustness properties of the continuous-time counterpart. Matching conditions under which the sliding mode is invariant to dynamical modelling errors and disturbances, and effects of measurement noise are also presented.

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Conference Proceedings of the 1995 American Control Conference. Part 1 (of 6)
Aitken, V, & Schwartz, H.M. (1995). Towards robust discrete-time sliding mode observers. In Proceedings of the American Control Conference (pp. 3730–3734).