Global stabilisation of large-scale hydraulic networks with quantised and positive proportional controls

The problem considered here is output regulation of a large-scale hydraulic network where the structure of the network is subject to change and where the actuation is subject to a non-negativity constraint. Previous results have shown that semi-global practical output regulation is achievable using a set of decentralised, logarithmic quantised and constrained control actions with properly designed quantisation parameters. That is, an attractor set with a compact basin of attraction exists. Subsequently, the basin can be increased by increasing the control gains. In our work, this result is extended by showing that an attractor set with a global basin of attraction exists for arbitrary values of positive control gains, given that the upper level of the quantiser is properly designed. Furthermore, the proof is given for general monotone quantisation maps. Since the basin of attraction is global and the result is independent on the size of the network, this shows that structural changes can be implemented without destabilising the closed-loop system.