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Different time-discretization methods for equivalent-control based slidingmode control (ECB-SMC) are presented. A new discrete-time sliding mode controlscheme is proposed for linear time-invariant (LTI) systems. It is error-free inthe discretization of the equivalent part of the control input. Results fromsimulations using the various discretized SMC schemes are shown, with andwithout perturbations. They illustrate the different behaviours that can beobserved. Stability results for the proposed scheme are derived.

Analysis of explicit and implicit discrete-time equivalent-control based sliding mode controllers