Authors\u27 Reply to Comments on A Novel Fault Diagnosis and Prediction Scheme using a Nonlinear Observer with Artificial Immune System as an Online Approximator

We realized that the statement of [1, Th. 2] must be revised since the mathematical derivations shown in [1, eq. (A.8)] only guarantees the first difference of the Lyapunov equation to be uniformly ultimately bounded (UUB) [2] without an additional stringent assumption which was inadvertently omitted. Therefore, in this note, we have revised the statement of Theorem 2, and only included the part of the proof that renders boundedness. In addition, we have provided clarifications regarding the use of Lemma 1. No other change is needed in other parts of the paper