Feedback control problems pertaining to the control of tensegrity robotic systems are detailed in this paper. The unique problems that arise due to the positivity of the string tensions required to maintain the static stability and desirable stiffness of the structural system are shown to bring about interesting opportunities to optimize for the redundancy in the actuation process. The static stability consideration, coupled with the nonlinear dynamics and the sensor models introduce additional algebraic constraints in implementation of both kinematic and model based dynamic controllers for tensegrity systems. Approaches to develop kinematic and dynamic control techniques are detailed in this paper. A bench top experimental setup consisting of a simple tensegrity system is utilized to demonstrate the efficacy of the output feedback control approach developed in the paper. Near real time image measurements are utilized to drive the output error used in the control scheme.