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

This paper presents a methodology for the design of observers for a family of Linear Time Varying systems with a single output satisfying a differential uniform observability property. To address the problem, an immersion of the original system in a higher-dimensional state space is proposed, where a bl-homogeneity (homogeneity in the bi-limit) based state observer is designed with theoretically exact convergence in finite-time. Furthermore, it is shown that, according to the selection of a set of parameters and gains, the convergence is in fixed-time.