Control of discrete-time nonlinear systems actuated through counter-convecting transport dynamics

Abstract

We consider the stabilisation of discrete-time nonlinear systems that are actuated through a pair of transport partial difference equation (PdE) systems that convect in the opposite directions from one another. An explicit feedback law that compensates the discrete PdE 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.