During decades, one of the most challenging hazards for civilizations has been the risk of seismic activity along with strong ground motion called earthquake. Many civil structures have been destroyed along with the civilization. Great improvements have been established in the exact analysis and design of high-rise buildings and wide-span bridges, subject to the vibrations of the earth. However, recently there have been considerable attentions to view these structures as dynamical systems and to control their intractable dynamics against the vibrational motions and dynamic loadings, instead of strengthening them. The challenging field of mechanical-structural vibration control of structures was gradually transferred from the field of civil and mechanical engineering to the control and system engineering community and attracted the attention of many researchers in these fields. This thesis focuses on the vibration control of a smart composite cantilever beam consisting of an elastic core layer as the host beam and two piezoelectric outer layers acting as the sensor and actuator. The For this purpose, in addition to the six mechanical degrees of freedom for every finite element, two additional electrical degrees of freedom were considered for the above-mentioned piezoelectric layers. The damping matrix is built up using the Rayleigh method. The vibration control of this structure is based on an electromechanical interaction of piezoelectric layers with elastic parts. Furthermore, unmodeled dynamics and future damages to the structure, which may cause some uncertainties in the structural parameters, are considered. In order to model these parametric uncertainties, the linear fractional transformation (LFT) method is used. The controller uses the µ-synthesis approach in order to reduce undesirable disturbances (dynamic loadings) and also to avoid closed-loop system instability caused by perturbations. In order to demonstrate the importance of the modeling of uncertainties, the process of designing an H ? -controller is presented for a nominal system at the first part of controller design, along with executing some numerical simulations for a corresponding nominal beam model. At the second part, the proposed µ-controller is presented for a perturbed beam model along with the related simulated results. At the end, some simulated results are presented for the case of two piezoelectric patches placed on just one of the finite elements near the foundation of the beam.