Stabilization of a tank via output feedback

We consider a tank containing fluid. The tank is subjected to a one-dimensional horizontal move and the motion of the fluid is described by shallow water equations. By means of a Lyapunov approach, we deduce the control laws to stabilize the state of the fluid-tank system. The control law is an output feedback where the output is given by the trajectory of the tank and the level of the fluid at the boundary of the tank. Although global asymptotic stability is yet to be proved, we numerically simulate the system and observe the stabilization.