LFT/SDP approach to the uncertainty analysis for state estimation of water distribution systems

A state estimator is an algorithm that computes the current state of a time-varying system from online measurements. Physical quantities such as measurements and parameters are characterised by uncertainty. Understanding how uncertainty affects the accuracy of state estimates is therefore a pre-requisite to the application of such techniques to real systems. In this paper a method of uncertainty analysis is developed based on linear fractional transformations (LFT) and ellipsoid-of-confidence bounds are obtained by recasting the LFT problem into a semidefinite programming problem (SDP). The ideas are illustrated by applying them to a simple example of a twelve-node water distribution network and the simulation results, obtained using the MATLAB mathematical package, are reported