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Hybrid system representations have been applied to many challenging modelling situations. In these hybrid system representations, a mixture of continuous and discrete states is used to capture the dominating behavioural features of a nonlinear, possible uncertain, model under approximation. Unfortunately, the problem of how to best design a suitable hybrid system model has not yet been fully addressed. This paper proposes a new joint state-measurement relative entropy rate based approach for this design purpose. Design examples and simulation studies are presented which highlight the benefits of our proposed design approaches.