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.
