Construction of 2D isomorphism for spatiotemporal L2-gain robust control

This work expands fundamental disciplines in classical control on 2D version to such an extent that the well-established 1D-H_infin robust control can be directly extended to spatiotemporal L₂-gain robust control for Sturm-Liouville class. The kernel is to extend Laplace transform and Fourier transform for Galerkin-Laplace transform and Galerkin- Fourier transform, respectively, which transform the spatiotemporally dynamics into pure algebra, and thus yield 2D frequency response served for spatiotemporal loopshaping. Moreover, to shape the loop using L₂-gain metric, the Small Gain Theorem together with its related issues is also revised to 2D version.