Corrigendum to “On stochastic and deterministic event-based state estimation” [Automatica 123 (2021) 109314] (Automatica (2021) 123, (S0005109820305148), (10.1016/j.automatica.2020.109314))

The purpose of this corrigendum is to correct a minor error in Proposition 2 in Yu, Shang, and Chen (2021), where the definition of [Formula presented] should be modified as[Formula presented] with [Formula presented]. That is, the coefficient [Formula presented] is added before the term [Formula presented]. This modification is to fix the incorrect definitions of [Formula presented] in line 5 of Case II and [Formula presented] in line 3 of Case III in the proof of Proposition 2 (in Appendix A.5). Actually, from Lemma 6 and the original definition of [Formula presented]: [Formula presented] one has the following relationship for [Formula presented] defined in line 2 of Case II: [Formula presented][Formula presented] which contradicts the desirable assertion, [Formula presented], in line 10 of Case II in the proof. This error stems from some misuse of Lemma 6 that itself is correct. When applying Lemma 6 to [Formula presented], we multiplied redundantly the coefficient [Formula presented] to the term [Formula presented]. By using Lemma 6 correctly, the definition of [Formula presented] in line 5 of Case II should be revised as [Formula presented] which ensures [Formula presented] Then, the proof of Proposition 2 in Case II (see Appendix A.5, page 12) is correct with the revised [Formula presented], since the analysis on the extremum of [Formula presented] is independent of the value of [Formula presented] (see the definition of [Formula presented] in line 14 of Case II). Subsequently, due to a similar reason, the definition of [Formula presented] in line 3 of Case III should be [Formula presented] which validates the proof of Case III in Proposition 2. While the final conclusion, Theorem 3, is correct as stated, its proof on page 7 requires adjustment to account for the modified Proposition 2. First, the definition of [Formula presented], in line 2 of the 2nd column of page 7, is revised as [Formula presented] with [Formula presented]. Consequently, Equation (22) should be written as [Formula presented] for [Formula presented].