  In this paper, we propose a second-order continuous primal-dual dynamical
system with time-dependent positive damping terms for a separable convex
optimization problem with linear equality constraints. By the Lyapunov function
approach, we investigate asymptotic properties of the proposed dynamical system
as the time $t\to+\infty$. The convergence rates are derived for different
choices of the damping coefficients. We also show that the obtained results are
robust under external perturbations.
