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In this paper, we design new sampled-data output feedback controllers to globally stabilise a class of high-order switched nonlinear systems in finite time under arbitrary switching. The switching signals exist in both the system powers and the nonlinear terms. First, we adopt the common Lyapunov function method to design a continuous-time output feedback controller. Then, the emulation method is used to construct the sampled-data output feedback controllers with a sampling period. Based on the homogeneity theory, Hölder inequality and Gronwall–Bellman inequality, the relationships between the sampling states (controllers) and the current states (controllers) are revealed. In the meantime, we obtain the sampling period for the sampled-data output feedback controllers to guarantee the global stabilisation of the closed-loop systems in finite time. Finally, a numerical example and a practical example are given to prove the efficiency of the proposed control method.

Sampled-data output feedback control for a class of high-order switched nonlinear systems