State Observation of Affine-in-the-States Systems with Unknown Time-Varying Parameters and Output Delay

Proposition 4 in the paper states the PEBO+DREM observer with the first-order filters, adjugate mixing, gradient law, and the clipped fixed-time transform, and proves fixed-time exact recovery under the IE condition together with boundedness of all signals; the candidate solution reproduces the same construction and error analysis step-by-step, adding minor clarifications (e.g., explicitly showing Y=Ωθ from the filtered regressions via zero initial conditions and a slightly sharper statement that the first threshold-crossing time tc satisfies tc ≤ tIE). Small notational mismatches (n+q vs n+k; reuse of Y) and the implicit zero-initialization of the filters are the only issues; they do not affect correctness. Hence both are correct and essentially the same proof .