3rd International Workshop on Linear Systems (LinSys2007)

Information Flows and Distributed Control
Girish Nair

This talk concerns the stabilisation of a linear plant with multiple controllers and noisy sensors over a digital network. Well-known results for the centralised case are first recapped. The distributed problem is then formulated, and a nearly necessary and sufficient condition for uniform stabilisability is presented in terms of the feasibility of a number of linear inequalities involving the unstable open-loop eigenvalues of the plant, the various channel data rates and the controllability/observability structures of the plant. This provides a nearly exact characterisation of the region of channel bit rate combinations that permit uniform stability to be achieved. The auxiliary variables introduced in the condition 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 also solves the classical problem of distributed stabilisability over all nonlinear, time-varying, causal policies.