Real-time hybrid simulation is an efficient and cost-effective experimental testing technique for performance evaluation of structural systems subjected to earthquake loading with rate-dependent behavior. To assess the response of structural components with multi-axial loading, a loading assembly with multiple parallel actuators connected to a rigid moving platform is required to impose realistic boundary conditions on physical components. This loading assembly is expected to exhibit significant dynamic actuator coupling and suffer from systematic errors and potential instabilities. One approach to reduce experimental errors considers a multi-input, multi-output (MIMO) modeling approach to design controllers that could compensate for these undesired effects. In this dissertation, a framework for three-dimensional, multi-axial real-time hybrid simulation is presented. The methodology consists in designing a real-time system platform to perform dynamic test experiments by controlling the interface boundary conditions on the physical specimen in Cartesian (global) coordinates. First, a kinematic transformation is derived to impose the six-degree-of-freedom motion to the loading platform in three-dimensional Cartesian space. Then, a linearized model of the multi-actuator loading assembly is obtained through nonparametric frequency domain system identification techniques. Subsequently, a feedforward-feedback compensator is developed for reference tracking of the multivariate transient signals, which should be sufficiently robust to rule out any disturbances and measurement noises in the experimental closed-loop system. Finally, the numerical substructure, compensators, and kinematic transformations are implemented over an embedded system with a micro-controller unit and digital signal processing capabilities for real-time applications. The proposed framework is validated using a small-scale version of the Load and Boundary Condition Box (LBCB) from Newmark Civil Engineering Laboratory at University of Illinois, Urbana-Champaign. A one-story, two-bay, moment frame was considered as the reference structure, where the experimental substructure was chosen as a steel column with fixed ends. The hybrid system was subjected to earthquake ground motions chosen according to its importance and destructive characteristics. Comparisons of different compensation strategies are made, and excellent performance is achieved for all situations that incorporates the multivariate controller.