Parameter Estimation of Two Classes of Nonlinear Systems with Non-separable Nonlinear Parameterizations ⋆

The PDF states the LS+DREM interlaced estimator, its signals Δ and 𝒴, and the global exponential convergence (GEC) claim under the interval excitation (IE) assumption A4 and an LMI monotonicity condition on W, but explicitly omits the proof and cites Ortega et al. (2022) for it. This makes the paper’s argument non-self-contained at the key step (the LS+DREM convergence proof) even though all definitions and assumptions are clearly presented in Proposition 1 and Assumption A4. The candidate solution fills precisely this gap: it proves the exact DREM identity 𝒴 ≡ Δ W(θ), shows Δ(t) acquires a uniform positive lower bound after the IE window, derives strong monotonicity from the LMI, and establishes an explicit exponential rate and overshoot via a Lyapunov inequality, while also checking boundedness of all internal signals. These steps align with the estimator and assumptions as defined in the paper (Assumption A4, Proposition 1, the LMI condition), but are not carried out in the PDF itself. One additional nuance the paper highlights for constructing the monotonic mapping in its system classes is the need for prior knowledge such as sign(θ1) and a bound used to select α; this is noted in the paper’s own discussion and is orthogonal to the LS+DREM convergence proof that the candidate provides. Therefore, the paper is correct in statement but incomplete in proof; the model’s solution is correct and completes the missing argument. Citations: the IE assumption and estimator are stated with definitions of Δ and 𝒴, and the proof is referenced to prior work; the scalar NLPRE form and LMI monotonicity appear in Section 4; the need for prior knowledge for TW/α selection is discussed in Lemma 2’s remarks.