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We propose a new design technique for the stabilization of coupled ODE-PDEsystems in feedforward form. In particular, we address the stabilizationproblem of a one-dimensional transport equation driven by a scalar ODE which iscontrolled via a cone-bounded nonlinearity. The unforced transport equation isconservative but not asymptotically stable. The proposed technique is inspiredby the forwarding approach early introduced in the 90's. Well-posedness andasymptotic stability of the closed-loop system are discussed.

Forwarding design for stabilization of a coupled transport equation-ODE with a cone-bounded input nonlinearity