A sliding mode observer with homogeneous estimation error for a class of linear time-invariant systems

This article presents a robust observer for a class of continuous-time linear time-invariant systems affected by unknown inputs. The sufficient conditions under which this observer allows the estimation error to possess the homogeneity property are studied. Furthermore, the observer algorithm comprises a linear compensation term that enables the observer nonlinear output injection term to provide global finite-time convergence despite bounded unknown inputs and system instability.