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Abstract This paper analyses the robust stability of a class of homogeneous systems where a relation among the high‐order term, the decay rate and the domain of attraction of the system is explicitly established. Such a new observation helps to establish several robust stability conditions for switched homogeneous systems with high‐order terms. Several domains of attraction related to asymptotical and finite‐time stability properties are also provided. The new results are further applied to supervisory control of spacecraft attitude system with high‐order uncertainties to illustrate their efficiency and applicability.