The research paper focuses on studying the robust stability and performance of suboptimal H_∞ control on mass-spring-dashpot systems subject to parametric uncertainty and external disturbance on output response. The objective is keeping the vertical oscillation of the system constant under uncertainty and disturbance. For the control system to achieve satisfactory performance, suitable weighting filter functions for performance and control effort were designed respectively. Model order reduction for the synthesized controller based on Hankel norm approximation was conducted where a third order controller is obtained. Numerical results based on µ-analysis, frequency response and transient response show that the closed-system achieved robust stability and robust performance to parametric uncertainty and disturbance at all frequencies over the entire frequency bandwidth of study.