High order sliding mode: is it useful in the design of observer under sparse measurement?

In this paper we investigate observer design under sparse measurement, i.e. under Nyquist-Shannon frequency. After an analysis which demonstrates the fact that it is impossible to use only a high order sliding mode observer, in the case of sparse measurement, it is shown that a high order sliding mode observer coupled with an impulsive observer is a pertinent solution at least for some particular class of systems. Simulation results highlight the interest of the proposed design.