CONSTRUCTION OF 2D ISOMORPHISM FOR 2D H∞-CONTROL OF STURM-LIOUVILLE SYSTEMS

This work makes possible that H-infinity-loopshaping has a 2D version for the Sturm-Liouville class of distributed parameter systems. Here, the Laplace integral is composite of a Galerkin projection to transform the underlying dynamics, both spatially distributed and temporally varying, into pure algebra, so that any technique of classical control becomes applicable to spatio-temporal analyses and syntheses. Accompanied by this Laplace-Galerkin transform and its inverse are Fourier-Galerkin transforms that constitute a pair of geometrical isomorphism between space-time domain and mode-frequency domain. Based on the isomorphism, Small Gain Theorem and H-infinity-loopshaping can expand on 2D version in terms of mode-frequency responses.