Sampled-Data Boundary Feedback Control of 1-D Parabolic PDEs

Abstract

The paper provides results for the application of boundary feedback control with Zero-Order-Hold (ZOH) to 1-D linear parabolic systems on bounded domains. It is shown that the continuous-time boundary feedback applied in a sample-and-hold fashion guarantees closed-loop exponential stability, provided that the sampling period is sufficiently small. Two different continuous-time feedback designs are considered: the reduced model design and the backstepping design. The obtained results provide stability estimates for weighted 2-norms of the state and robustness with respect to perturbations of the sampling schedule is guaranteed.

22 pages, submitted to Automatica for possible publication

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• Input-to-State Stability with Respect to Boundary Disturbances for a Class of Semi-linear Parabolic Equations
• Sampled-Data Boundary Feedback Control of 1-D Hyperbolic PDEs with Non-Local Terms