Many people are affected by a wide range of neuromuscular disorders, many of which can be improved through the use of Functional Electrical Stimulation (FES) rehabilitative cycling. Recent improvements in nonlinear, Lyapunov-based FES muscle control with motor assistance in unstimulated regions of the cycle-crank rotation have led to a reduction in muscle fatigue, allowing rehabilitation time to be extended. Studies in rehabilitation have shown that the addition of coordinated movement between the upper limbs and lower limbs can have a positive effect on neural plasticity leading to faster restoration of walking in those who have some neurological disorders. In this paper, to implement coordinated motion during rehabilitation, a strongly coupled bilateral telerobotic system is developed between a hand-cycle system driven by the participant’s volitional efforts and a split-crank leg-cycle system driven by the switched application of FES with motor assistance. A variable operator is applied to the leg-cycle’s motor input during the FES stimulation regions to provide assistance as required. Lyapunov-based analysis methods are used on the combined leg and hand-cycle system to prove global exponential stability. Analysis further proves that all switched system inputs are bounded, thus the states of the telerobotic master (i.e., hand-cycle system) are bounded, therefore, the telerobotic system is stable.