Continuous-time stable and unstable system modelling with orthonormal basis functions

Abstract

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 < infinity) 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 < infinity. Some inequalities on the l(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 (C) 2000 John Wiley & Sons, Ltd.