Sampled-Data Boundary Feedback Control of 1-D Hyperbolic PDEs with Non-Local Terms
Provides theoretical guarantees for sampled-data control of hyperbolic PDEs, addressing a gap in control theory for non-local terms.
This paper proves that boundary feedback control with Zero-Order-Hold sampling stabilizes 1-D hyperbolic PDEs with non-local terms, achieving exponential stability with arbitrarily fast convergence rate as sampling period decreases, unlike parabolic systems.
The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear, first-order, hyperbolic systems with non-local terms on bounded domains. 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.