Decentralised state feedback stabilisation for nonlinear interconnected systems using sliding mode control

In this paper, the stabilisation problem is considered for a class of nonlinear interconnected systems with matched uncertainties and mismatched unknown interconnections. A composite sliding surface is designed firstly, and a set of conditions is developed to guarantee that the corresponding sliding motion is uniformly asymptotically stable. Then, decentralised state feedback sliding mode control is proposed to drive the interconnected systems to the designed sliding surface in finite time, and a sliding motion is maintained thereafter. The bounds on the uncertainties and interconnections have more general nonlinear forms, which are employed in the control design to reject the effects of uncertainties and unknown interconnections to enhance the robustness. It is not required either the isolated nominal subsystems linearisable or the interconnections linearisable. Finally, a numerical simulation example is presented to demonstrate the effectiveness of the proposed control strategy.