arXiv:2610.29656v1 Announce Type: new Abstract: This paper develops a procedure for designing discrete-time distributed algorithms to achieve a desired collective behavior. Each agent combines its node and coupling updates at every iteration, in either explicit or implicit form. For this structure, we derive necessary and sufficient conditions on the local parameters for realizing a desired continuous-time blended dynamics. These conditions yield a decentralized procedure for computing the parameters. A Tikhonov-type approximation result relates the resulting agent trajectories to the blended dynamics on a rescaled time axis. Under a stability condition imposed only on the blended dynamics, we further establish uniform-in-time approximation bounds. We also characterize the trade-off between approximation accuracy and the iteration count guaranteed by these bounds. The framework is illustrated through four applications in distributed computation and estimation.