Abstract
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 closed-loop 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 sup-norm of the state and robustness with respect to perturbations of the sampling schedule is guaranteed.
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