  Drinking water distribution networks (WDN) are large-scale, dynamic systems
spanning large geographic areas. Water networks include various components such
as junctions, reservoirs, tanks, pipes, pumps, and valves. Hydraulic models for
these components depicting mass and energy balance form nonlinear algebraic
differential equations (NDAE). While control theoretic studies have been
thoroughly explored for other complex infrastructure such as power and
transportation systems, little is understood or even investigated for feedback
control and state estimation problems for the NDAE models of WDN. The objective
of this letter is to showcase a complete NDAE model of WDN followed by
computing Lipschitz constants of the vector-valued nonlinearity in that model.
The computation of Lipschitz constants of hydraulic models is crucial as it
paves the way to apply a plethora of control-theoretic studies for water system
applications. In particular, the computation of Lipschitz constant is explored
through closed-form, analytical expressions as well as via numerical methods.
Case studies reveal how such computations fare against each other for various
water networks.
