On Boundary Control of the Transport Equation. Assigning Real Spectra and Exponential Decay

Recently, an intriguing property called coexistent-real-roots-induced-dominancy (CRRID) has been set and emphasized for some classes of linear time-invariant dynamical systems represented by retarded delay-differential equations. In this letter, we extend such a property to a class of neutral systems, and exploit it in the boundary control of the standard transport equation. Namely, by using the CRRID property, we show that one can arbitrarily and robustly prescribe the exponential decay of the closed-loop transport solution, yielding the prospect of applying the CRRID partial poles placement methodology to hyperbolic PDE’s.