An LFT/SDP Approach to the Uncertainty Analysis for State Estimation of Water Distribution Systems Atulya K. Nagar and Roger S. Powell Department of Systems Engineering, Brunel University, Uxbridge UB8 3PH, U.K. [atulya.nagar, roger.powell]@brunel.ac.uk Abstract A state estimator is an algorithm that computes the current state of a time-varying system from on-line 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 we develop a method of uncertainty analysis based on linear fractional transformations (LFT) and obtain ellipsoid-of-confidence bounds by recasting the LFT problem into a semidefinite programming problem (SDP). The ideas are illustrated by applying them to a simple water distribution network. 1 Introduction State estimation is defined as the computation of the minimum set of values necessary to completely describe all other pertinent variables in a given system from some measurement data [19]. When applied to water or gas distribution networks it can be viewed as an on-line monitoring system capable of tracking the time varying flows and pressures in real-time. In power systems, voltages and power flows can be estimated. The state estimator algorithm maps the available new information (from measurements) into a state- space using an over-determined set of (non-linear) equations. This is typically formulated as a projection resulting in a minimisation problem, e.g. weighted least squares (WLS). In general, static state-estimation can be categorised according to the minimisation cost function used; either a quadratic, e.g. weighted least squares, or a non-quadratic function. A great number of papers on power systems state estimation have concentrated on variations on the WLS theme by including different methods of bad data detection and identification. Examples include identification by elimination [22], hypothesis testing identification [15], 1