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Section: New Results

Discrete-time sliding mode control

Participants : Vincent Acary, Bernard Brogliato, Olivier Huber, Bin Wang.

This topic concerns the study of time-discretized sliding-mode controllers. Inspired by the discretization of nonsmooth mechanical systems, we propose implicit discretizations of discontinuous, set-valued controllers. This is shown to result in preservation of essential properties like simplcity of the parameters tuning, suppression of numerical chattering, reachability of the sliding surface after a finite number of steps, and disturbance attenuation by a factor $h$ or $h^2$ [18] . In [23] we have provided a tutorial on similar types of systems like relay systems, and their relationships with other formalisms like complementarity systems, or switching dynamical systems. This follows in fact a research program proposed in [4] .