Cooperative networked stabilisability of linear systems with measurement noise

This paper investigates the problem of stabilising a linear, time-invariant plant with multiple controllers and noisy sensors over a digital network. A necessary and (almost) sufficient condition for determining networked uniform stabilisability, is derived, in terms of the feasibility of a set of linear inequalities involving the unstable eigenvalues of the plant and the various channel data rates. This provides a nearly exact characterisation, up to boundary points, of the region of all channel data rate combinations that permit uniform stability to be achieved. The auxiliary variables in this characterisation have a natural interpretation as the effective rates of information flow through the network, associated with each unstable mode. When channel rates are set to either zero or infinity, this agrees with a classical result on decentralised stabilisability under linear time-varying control.