Enhanced matching perturbation attenuation with discrete-time implementations of sliding-mode controllers

Continuous-time Sliding Mode Control yields when embedded into Filippov´s mathematical framework, closed-loop systems with a set-valued controller, represented by differential inclusions. In particular, besides finite-time convergence to the sliding surface and robustness to matched disturbances, such controllers allow an exact compensation of the disturbance on the sliding manifold. In other words, the set-valued input is the exact copy of minus the perturbation. A novel discretization methodology has been recently introduced by the authors, which is based on an implicit discretization of the Filippov´s differential inclusion, which in theory totally suppresses the chattering due to the discretization (numerical chattering). In this work we propose an extension of the implicit method, enhancing the perturbation attenuation (in terms of chattering) by using previous values of the set-valued input. This allows to estimate on-line the unknown perturbation, with a time delay due to the sampling. Simulation results illustrate the effectiveness of the method.