This paper investigates the robust semiglobal containment control problem for multi-agent systems composed of linear agents with heterogeneous parameter uncertainties and input saturation constraints. A novel low-gain-based nonlinear containment control algorithm is proposed and analyzed. Theoretical analysis demonstrates that the semiglobal containment control objective can be achieved when the relationship between the lower bound of input saturation and the upper bound of parameter uncertainties satisfies specific conditions, which are explicitly characterized as design constraints in the proposed method. Furthermore, the control protocol is extended to an event-triggered framework, incorporating both the containment control law design and node-based event-driven updating mechanisms.