Aperiodic Sampled-Data Distributed Observer Design

The paper proves exponential convergence of the distributed sampled‑data observer via a hybrid/discretization and ISS argument, yielding explicit bounds hmax = min{τ1(χ, κ), τ0} together with γ ≥ γmax, as stated in Algorithm 1 and Theorem 1. The candidate solution establishes the same main claim under the same standing assumptions (strong connectivity and joint observability), but with a different proof sketch: (i) per‑node Kalman decomposition; (ii) small‑gain/L2 analysis for the observable blocks to get τ1(χ, κ); (iii) an ISS Lyapunov estimate for the unobservable blocks to get τ0; and (iv) a composite Lyapunov function to conclude exponential stability. Substantive agreements include the structure of the error dynamics in observability coordinates, the role of the symmetrized Laplacian with Θ, the explicit forms of γmax, τ0 and τ1, and the final stability claim (; ; ; ). The main discrepancy is that the model’s Step 2b omits the sampled coupling term −γ V_u^T (L ⊗ I) V_o ξ_o(t_k) that appears in the paper’s stacked u‑dynamics and is handled in the paper via a discrete‑time “input” term g(t_k) (; ). This omission affects intermediate bounds (e.g., c2) but not the final conclusion; incorporating this term as an additional vanishing input preserves the model’s overall argument. Hence, both are correct, with different proof routes, and the model needs a minor patch to its Step 4 bounds.