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Presented is a novel and analytical approach to design a hybrid controller based on hybrid zero dynamics for exponential stabilisation of a desired periodic orbit for a hybrid model of walking composed of single and double support phases. To achieve this goal, the effect of a double support phase on angular momentum transfer and stabilisation is investigated. Also, the class of control inputs corresponding to an orbit during double support is presented. A smooth feedback law based on a radial basis function network is then proposed for the double support phase such that (i) the desired orbit is exponentially stable and (ii) the control vector minimises the least square control cost.