Network observability: Theory and algorithms based on triangular factorisation and path graph concepts

A theory is developed to test network observability, to identify possible subnetworks which might be observable, and, in case the network is not observable, to identify the minimal set of measurements (pseudo) to be added so that the network as a whole becomes observable. Algorithms to test network observability and to identify subnetworks of the entire system that might be observable are also presented. An algorithm to add a minimal set of measurements to the existing measurements, so that the network becomes observable as a whole, is developed. The theory and algorithms that result are a combination of factorisation path concepts and triangularisation of the gain matrix G. Such algorithms have the characteristics of being very simple, easy to implement, extremely fast and reliable. Algorithms resulting from this theory do not require solutions of any algebraic equation.