Bl-homogeneous observer for differentially uniformly observable LTV systems with a single output

In this paper, we introduce a family of fixed-time converging state observers tailored for a specific class of linear time-varying systems (LTV) featuring a single output. This class, termed Differentially Uniformly Observable (DUO), is defined by possessing an observability matrix of finite order, possibly larger than system's dimension, with full-column rank over a designated time interval. For analytic systems, this characteristic is essentially synonymous with observability. We demonstrate the seamless immersion of the system into a higher dimensional system in observability normal form. Furthermore, our proposed observer ensures global and exact convergence within a finite or fixed time frame.