We strive to prove stability of a hydraulic network,where the pressure at the end user is controlled with PIcontrol. The non-polynomial model is represented by numerouspolynomial systems defined on sub-sets of R^n. The sub-sets aredefined by compact basic semi-algebraic sets. The stability ofthe PI-controller is proved by designing a Lyapunov functionwhich fulfils different criteria in different sub-sets of R^n. Wefind a polynomial Lyapunov function for the system usingSOSTOOLS supported by Putinar’s Positivstellensatz.