Discrete time supper-twisting observer for 2n dimensional systems

Sliding Mode theory has attracted the attention of many researchers due to its remarkable characteristics. A substantial amount of research is carried out in continuous time for the conventional sliding mode theory and subsequently for second order sliding modes. However, for the discrete time, case, this theory has not been exploited in comparison with the continuous case, especially for the high order sliding mode theory, There are some results about the problem of observation for discrete systems using techniques such as finite differences. In most cases, the results may only prove exponential convergence to a region delimited by the sampled period. This article proposes an observer based on the super twisting algorithm for discrete-time systems 2n dimensional. The stability proofs are given in the discrete Lyapunov sense. In terms of the linear matrix inequalities theory, the error trajectories are ultimately bounded in finite time. We present numerical results of the observer in a nonlinear biped model obtained from a discretization using the Euler approximation.