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Human-robot interaction (HRI) for gait rehabilitation would benefit from models of data-driven gait models that account for gait phases and gait dynamics. Here we address the current limitation in gait models driven by kinematic data, which do not model interlimb gait dynamics and have not been shown to precisely identify gait events. We used Switched Linear Dynamical Systems (SLDS) to model joint angle kinematic data from healthy individuals walking on a treadmill with normal gaits and with gaits perturbed by electrical stimulation. We compared the model-inferred gait phases to gait phases measured externally via a force plate. We found that SLDS models accounted for over 88% of the variation in each joint angle and labeled the joint kinematics with the correct gait phase with 84% precision on average. The transitions between hidden states matched measured gait events, with a median absolute difference of 25ms. To our knowledge, this is the first time that SLDS inferred gait phases have been validated by an external measure of gait, instead of against predefined gait phase durations. SLDS provide individual-specific representations of gait that incorporate both gait phases and gait dynamics. SLDS may be useful for developing control policies for HRI aimed at improving gait by allowing for changes in control to be precisely timed to different gait phases.