Based on the Lyapunov stability theorem, a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper. This scheme is implemented for a class of large-scale systems with both matched and mismatched perturbations. The perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions. The decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem, so that when each subsystem enters the sliding mode, the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability. The decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time. This is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels. A numerical example is included to demonstrate the feasibility of the proposed control scheme.