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We study a feedback stabilization problem for a first-order hyperbolicpartial differential equation. The problem is inspired by the stabilization ofequilibrium age profiles for an age-structured chemostat, using the dilutionrate as the control. Two distinguishing features of the problem are that (a)the PDE has a multiplicative (instead of an additive) input and (b) the stateis fed back to the inlet boundary. We provide a sampled-data feedback thatensures stabilization under arbitrarily sparse sampling and that satisfiesinput constraints. Our chemostat feedback does not require measurement of theage profile, nor does it require exact knowledge of the model.

Ergodic Theorem for Stabilization of a Hyperbolic PDE Inspired by Age-Structured Chemostat