Modern aircraft designers are adopting light-weight, high-aspect ratio flexible wings to improve performance and reduce operation costs. A technical challenge associated with these designs is that the large deformations in flight of the wings lead to adverse interactions between the aircraft aerodynamic forces and structural forces. These adverse interactions produce excessive vibrations that can degrade flying qualities and may result in severe structural damages or catastrophic failure. This dissertation is focused on the application of multivariable robust control techniques for suppression of these adverse interactions in flexible aircraft. Here, the aircraft coupled nonlinear equations of motion are represented in the linear, parameter-varying framework. These equations account for the coupled aerodynamics, rigid body dynamics, and deformable body dynamics of the aircraft. Unfortunately, the inclusion of this coupled dynamics results in high-order models that increase the computational complexity of linear, parameter-varying control techniques. This dissertation addresses three key technologies for linear, parameter-varying control of flexible aircraft: (i) linear, parameter-varying model reduction; (ii) selection of actuators and sensors for vibration suppression; and (iii) design of linear, parameter-varying controllers for vibration suppression. All of these three technologies are applied to an experimental research platform located at the University of Minnesota. The objective of this dissertation is to provide to the flight control community with a set of design methodologies to safely exploit the benefits of light-weight flexible aircraft.