Semi-global stabilization of a nonlinear transport equation with nonlocal velocity∗

In this paper, we establish the semi-global feedback stabilization for a class of nonlinear transport equations with nonlocal velocity, which models a highly re-entrant system encountered in semi-conductor manufacturing. We design two new time-varying feedback laws: one yields a semi-global exponential stability of the corresponding closed-loop system, the other one yields a local exponential stability result for the corresponding closed-loop system. The crucial assumption on the velocity function λ(·) and the target equilibrium ρ is strongly reduced compared to the previous results. Numerical simulations are also provided as illustration of the theoretical results.