Robust vibration control of flexible appendant structures on a rigid base was investigated. The Structured Singular Value(μ) theory was applied to design a robust vibration controller, and piezoelectric patches were used as actuators and sensors. Output multiplicative uncertainty structure was adopted to depict the discrepancies between nominal model and real system, and μ controller synthesis framework was formed. A flexible beam appended to a rigid base was taken as an example to illustrate the μcontroller design process. The simulation results showed that the μ controller exhibited good performance. So, it's feasible to apply Structured Singular Value theory in vibration control of flexible appendant structures.