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In this study, an extended backstepping approach is developed for tracking control of a class of systems that are globally diffeomorphic into systems in generalised output feedback canonical form. Output-dependent non-linearities are allowed to enter such a system both additively and multiplicatively. The system contains unknown parameters multiplied by output-dependent non-linearities. This method relies on a parameter estimator and state observer design and standard backstepping construction. Compared with the traditional parameter estimation and state observation, the approach in this study has three distinct features due to adopting the new adaptive mechanism recently developed in literature. First, the parameter estimator and state observer does not follow the classical certainty equivalent principle. Second, the design treats the unknown parameter estimation and unmeasured state observation in a united way. Third, unlike the conventional observer-based backstepping, the design does not require the construction of Lyapunov function for every augmented sub-system. Furthermore, the method is applied to the stabilisation of single-machine-infinite-bus power systems with steam valve control using only measurements of the power angle as an illustrative example. A typical example is also given to show that the proposed method can be applied to more general systems which violate the cascading upper diagonal dominance conditions.