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

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 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 © 2000 John Wiley & Sons, Ltd.