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This work explores a method for analytically computing the infinites-imal phase response curves (iPRCs) of a synthetic nervous system (SNS) for a hybrid exoskeleton. Phase changes, in response to perturbations, revealed by the iPRCs, could assist in tuning the strength and locations of sensory pathways. We model the SNS exoskeleton controller in a reduced form using a state-space rep-resentation that interfaces neural and motor dynamics. The neural dynamics are modeled after non-spiking neurons configured as a central pattern generator (CPG), while the motor dynamics model a power unit for the hip joint of the exoskeleton. Within the dynamics are piecewise functions and hard boundaries (i.e. “sliding conditions”), which cause discontinuities in the vector field at their boundaries. The analytical methods for computing the iPRCs used in this work apply the adjoint equation method with jump conditions that are able to account for these discontinuities. To show the accuracy and speed provided by these methods, we compare the analytical and brute-force solutions.