Stability of a Class of Controllers for a Sequence of Canals and Structures

Networks of open channels form an important category of environmental systems. They are used not only to transport irrigation and drainage water, but also as highways for barges transporting raw materials and goods. Automatic control of these systems poses specific problems. A local stability analysis for an open canal that is split into several parts by sluice gates under discrete time control is proposed. Theoretical justification is provided, and the method is tested for a simple controller. The method allows the examination of local stability of a series of canals when equipped with a controller from a large class, linear and non-linear. The analysis is based on the analysis of the eigenvalues of a matrix derived from the controlled system that is small enough to allow for parameter optimization.