In this paper, model sets for linear time-invariant continuous-time systems
which are spanned by fixed-pole orthonormal bases are investigated. The ob
tained model sets are shown to be complete in the Lebesque spaces L-p (1 <
p < infinity) and in C, the space of complex-valued functions that are cont
inuous on the extended imaginary axis. The L-p norm error bounds for estima
ting systems in L-p by the partial sums of the Fourier series formed by the
orthonormal functions are computed for the case 1 < p < infinity. Some ine
qualities on the l(p) means of the Fourier coefficients are also derived. T
hese results have application in estimation and model reduction of stable a
nd unstable continuous-time linear time-invariant systems. A numerical exam
ple illustrates the use of the basis functions for the approximation of uns
table infinite-dimensional dynamics. Copyright (C) 2000 John Wiley & Sons,
Ltd.