Global decentralised stabilisation for a class of uncertain large-scale high-order upper-triangular nonlinear systems

This paper considers the global decentralised stabilisation problem for a class of uncertain large-scale high-order upper-triangular nonlinear systems. First, a local linear decentralised controller is recursively constructed based on the generalised homogeneous system theory and the adding a power integrator method. Second, aiming for global stabilisation, a series of nested saturation functions are integrated with the proposed local linear decentralised controller. Then, it is proved that the obtained decentralised saturated controller will render the whole closed-loop system globally asymptotically stable. Due to the flexibility of the generalised homogeneous method, the proposed control approach not only weakens the existing restrictions imposed on the interconnected nonlinearities, but also can be applied to a more general class of upper-triangular nonlinear systems. Furthermore, two simulations examples are conducted to show the effectiveness of the proposed control scheme.