Nonlinear control under discrete transport PdEs on domains of time-varying length

We consider the stabilization of discrete-time nonlinear OdE systems under discrete transport PdEs which convect in opposite directions. An explicit feedback law that compensates discrete transport PdEs actuator dynamics is designed. Global asymptotic stability of the closed-loop system is proved with the aid of a Lyapunov function. The feedback design is illustrated through an example. The proposed design in this paper allows the delay to be arbitrarily long and time-varying. Furthermore, our predictor feedback law in discrete time is explicit as the predictor state is computed by an algebraic equation.