Explicit Backstepping Kernel Solutions for Leak Detection in Pipe Flow Networks Containing Loops

Abstract

A recursive procedure to obtain explicit expressions to a set of observer backstepping kernel equations for an interconnection (cascade) of N + 1 systems of 2 × 2 linear hyperbolic PDEs, N > 0 an integer, for use in leak detection in pipe flow networks containing loops is developed. The kernel equations, consisting of two sets each of N + 1 pairs of Goursat PDEs defined over a triangular domain, and