Finite-Time State-Observer for a Class of Linear Time-Varying Systems with Unknown Inputs

A finite-time observer for a class of linear time-varying systems with bounded unknown inputs is presented in this note. The design of the observer exploits structural properties of the system and, through a linear operator, allows applying the robust-exact differentiator in a block form without requiring additional stabilizing terms. The proposed observer provides an exact estimate of the states after a finite transient-time despite the possible instability of the system and the effects of bounded unknown inputs.