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Continuous‐time stable and unstable system modelling with orthonormal basis functions
Author(s) -
Akçay Hüseyin
Publication year - 2000
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/(sici)1099-1239(200005)10:6<513::aid-rnc490>3.0.co;2-o
Subject(s) - orthonormal basis , basis (linear algebra) , mathematics , basis function , control theory (sociology) , computer science , mathematical analysis , control (management) , physics , geometry , artificial intelligence , quantum mechanics
In this paper, model sets for linear time‐invariant continuous‐time systems which are spanned by fixed‐pole orthonormal bases are investigated. The obtained model sets are shown to be complete in the Lebesque spaces L p (1< p <∞) and in C , the space of complex‐valued functions that are continuous on the extended imaginary axis. The L p norm error bounds for estimating systems in L p by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1< p <∞. Some inequalities on the p means of the Fourier coefficients are also derived. These results have application in estimation and model reduction of stable and unstable continuous‐time linear time‐invariant systems. A numerical example illustrates the use of the basis functions for the approximation of unstable infinite‐dimensional dynamics. Copyright © 2000 John Wiley & Sons, Ltd.