Premium
Construction of 2D isomorphism for 2D H ∞ ‐control of Sturm‐Liouville systems
Author(s) -
Hong BoeShong
Publication year - 2010
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.176
Subject(s) - laplace transform , mathematics , isomorphism (crystallography) , galerkin method , fourier transform , domain (mathematical analysis) , uniqueness , mathematical analysis , pure mathematics , inverse , projection (relational algebra) , algorithm , geometry , finite element method , physics , chemistry , crystal structure , thermodynamics , crystallography
This work makes possible that H ∞ ‐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 ∞ ‐loopshaping can expand on 2D version in terms of mode‐frequency responses. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society