In this paper, the state-space averaged small-signal model is derived for a non-isolated single-input-multi-output (SIMO) DC-DC converters. When the dynamics of the converters are governed by switched ordinary differential equations (ODEs), the averaged model can be derived through traditional methods. The modelling challenge in non-isolated SIMO converter arises from the differential algebraic nature of the circuit. Here the traditional methods cannot directly be applied. This is addressed using the quasi-Weierstrass transformation (QWT) which transforms the switched DAE system to an equivalent switched ODE system. A small-signal averaged model is obtained for the transformed switched ODE system using the notion of consistency projectors. We take the Zeta-Buck-Boost converter (ZBB) as an example and derive the small signal state-space averaged model for it. Simulations are performed to compare the time-response of the states corresponding to the switching circuit and the small-signal averaged model. A hardware setup of Zeta-Buck-Boost converter is designed and the proposed dynamic model is verified experimentally. © 2018 IEEE.