Control of shallow waves of two unmixed fluids by backstepping

Among the existing global challenges, water system management is becoming more and more important as the consumption patterns are continually growing. The implication of water system regulation in irrigated agriculture and production of sustainable energy is self-evident nowadays. In the present paper, new perspectives are given on the control of water flowing in an open channel. Mathematically, these physical processes are described by coupled hyperbolic partial differential equations (PDEs). In view of the recent development in PDE control, backstepping methodology has been proven to be a powerful tool in the sense that it provides a systematic design technique. This paper presents the exponential stabilization results of two shallow wave systems including the shallow waves of two unmixed fluids.