Sampled-data boundary feedback control of 1-D linear transport PDEs with non-local terms

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D inhomogeneous, linear, transport partial differential equations on bounded domains with constant velocity and non-local terms. It is shown that the emulation design based on the recently proposed continuous-time, boundary feedback, designed by means of backstepping, guarantees closedloop exponential stability, provided that the sampling period is sufficiently small. It is also shown that, contrary to the parabolic case, a smaller sampling period implies a faster convergence rate with no upper bound for the achieved convergence rate. The obtained results provide stability estimates for the supnorm of the state and robustness with respect to perturbations of the sampling schedule is guaranteed. © 2017 Elsevier B.V. All rights reserved.