This paper discusses the sampled-data consensus problem of multi-agent systems with general linear dynamics and time-varying sampling intervals. To investigate the allowable upper bound of sampling intervals, we employ the property of discretization of sampled-data to identify the upper bound on the variable sampling intervals via a continuous-time model. Without considering the states in the sampling intervals, the decrease of Lyapunov function is guaranteed only at each sampling time. Consequently, it results in a more robust sampling interval which is obtained by verifying the feasibility of LMIs. Subsequently, provided a limited matrix variable, the control gain matrix K is solved by the LMI approach. Numerical simulations are provided to demonstrate the effectiveness of theoretical results.