# ISS with Respect to Boundary Disturbances for 1-D Parabolic PDEs

@article{Karafyllis2016ISSWR, title={ISS with Respect to Boundary Disturbances for 1-D Parabolic PDEs}, author={I. Karafyllis and M. Krsti{\'c}}, journal={IEEE Transactions on Automatic Control}, year={2016}, volume={61}, pages={3712-3724} }

Due to unbounded input operators in partial differential equations (PDEs) with boundary inputs, there has been a long-held intuition that input-to-state stability (ISS) properties and finite gains cannot be established with respect to disturbances at the boundary. This intuition has been reinforced by many unsuccessful attempts, as well as by the success in establishing ISS only with respect to the derivative of the disturbance. Contrary to this intuition, we establish such a result for… CONTINUE READING

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