Robust hybrid observer design based on reconstructability conditions for piecewise linear systems

In this article, a robust hybrid observer is proposed to estimate the state of piecewise linear systems (PWL) that fulfill the reconstructability conditions. The design of this observer uses a high order sliding mode differentiator and is based on the reconstructability conditions for the discrete state of PWL systems. Additionally, the design takes into account the case when the differentiator output does not converge exactly to the actual derivatives of the system output. This could be due to the system output being affected by unknown but bounded perturbations or the differentiator being implemented on a digital device. The applicability of the results is illustrated by a numerical example.