Observer Design for the State Estimation of Epidemic Processes

The paper proves asymptotic stability of the proposed observer’s error dynamics under either a Lipschitz bound (Theorem 1, ARI (17)) or a generalized Lipschitz bound (Theorem 3, ARI (22)), by choosing V(e)=e^T P e and bounding the cross term via Cauchy–Schwarz/Young-type inequalities; see the observer/error dynamics (14)–(16) and the derivative expression (18), followed by the Lipschitz estimate (13) and the generalized version using Lemma 2, culminating in (17) and (22) respectively . The candidate solution reproduces precisely this Lyapunov argument: it defines M and N, derives ė = M e + N G Δf, applies Young’s (weighted) inequality to 2 e^T P N G Δf, and invokes the (generalized) Lipschitz bound to obtain a negative-definite quadratic upper bound on V̇, hence exponential (in particular asymptotic) convergence. Minor issues: the candidate calls the Riccati-type matrix inequality an “LMI” (the paper calls it an ARI, later converted to LMIs via an equivalent reformulation), and it omits the paper’s standing detectability assumption for (A,C) that motivates choosing J so M can be Hurwitz . These are presentation, not correctness, issues.